[Samsung Galaxy S5 Neo ROMs, Kernels, Recoveries, &] Zeh John:
Thank you so much for your reply, @Beta123MAX.

I have installed Heimdall v1.4.2 from Linux Mint 21.3's repositories.

(I've checked his website and the newest version I found there was 1.4.0, from 2013, weird. Mint's version is from 2017. I have used the terminal text version)

With the phone on Download Mode, heimdall print-pit gave a long list of partitions, apparently with no errors and then rebooted automatically.

I restarted the phone again into Download Mode and executed:

heimdall flash --RECOVERY twrp-3.7.0_9-0-s5neolte-unofficial-newsources.img

It's output:

Initialising connection...
Detecting device...
Claiming interface...
Setting up interface...

Initialising protocol...
Protocol initialisation successful.

Beginning session...

Some devices may take up to 2 minutes to respond.
Please be patient!

Session begun.

Downloading device's PIT file...
PIT file download successful.

Uploading RECOVERY
100%
RECOVERY upload successful

Ending session...
Rebooting device...
Releasing device interface...

So no errors, apparently. And then the phone rebooted.

Rebooted the phone into Recovery Mode but I still have LineageOS' Recovery, not TWRP.

Here's heimdall print-pit's output AFTER trying to flash TWRP. I'm sorry I didn't save the before's one.

heimdall print-pit
Heimdall v1.4.2

Copyright (c) 2010-2017 Benjamin Dobell, Glass Echidna
http://www.glassechidna.com.au/

This software is provided free of charge. Copying and redistribution is
encouraged.

If you appreciate this software and you would like to support future
development please consider donating:
http://www.glassechidna.com.au/donate/

Initialising connection...
Detecting device...
Claiming interface...
Setting up interface...

Initialising protocol...
Protocol initialisation successful.

Beginning session...

Some devices may take up to 2 minutes to respond.
Please be patient!

Session begun.

Downloading device's PIT file...
PIT file download successful.

Entry Count: 27
Unknown 1: 1598902083
Unknown 2: 844251476
Unknown 3: 21324
Unknown 4: 14153
Unknown 5: 14389
Unknown 6: 48
Unknown 7: 0
Unknown 8: 0

--- Entry #0 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 80
Attributes: 2 (STL Read-Only)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 0
Partition Block Count: 8192
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: BOOTLOADER
Flash Filename: sboot.bin
FOTA Filename:

--- Entry #1 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 90
Attributes: 2 (STL Read-Only)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 0
Partition Block Count: 8192
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: CM
Flash Filename: cm.bin
FOTA Filename:

--- Entry #2 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 70
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 34
Partition Block Count: 16
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: PIT
Flash Filename: -
FOTA Filename:

--- Entry #3 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 71
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 50
Partition Block Count: 2048
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: MD5HDR
Flash Filename: md5.img
FOTA Filename:

--- Entry #4 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 1
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 8192
Partition Block Count: 8192
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: BOTA0
Flash Filename: -
FOTA Filename:

--- Entry #5 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 2
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 16384
Partition Block Count: 8192
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: BOTA1
Flash Filename: -
FOTA Filename:

--- Entry #6 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 3
Attributes: 5 (Read/Write)
Update Attributes: 5 (FOTA)
Partition Block Size/Offset: 24576
Partition Block Count: 40960
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: EFS
Flash Filename: efs.img
FOTA Filename:

--- Entry #7 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 4
Attributes: 5 (Read/Write)
Update Attributes: 5 (FOTA)
Partition Block Size/Offset: 65536
Partition Block Count: 16384
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: CPEFS
Flash Filename: cpefs.img
FOTA Filename:

--- Entry #8 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 5
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 81920
Partition Block Count: 8192
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: m9kefs1
Flash Filename: m9kefs1.bin
FOTA Filename:

--- Entry #9 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 6
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 90112
Partition Block Count: 8192
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: m9kefs2
Flash Filename: m9kefs2.bin
FOTA Filename:

--- Entry #10 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 7
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 98304
Partition Block Count: 8192
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: m9kefs3
Flash Filename: m9kefs3.bin
FOTA Filename:

--- Entry #11 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 8
Attributes: 5 (Read/Write)
Update Attributes: 5 (FOTA)
Partition Block Size/Offset: 106496
Partition Block Count: 2048
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: CARRIER
Flash Filename: carrier.img
FOTA Filename:

--- Entry #12 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 9
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 108544
Partition Block Count: 16384
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: PARAM
Flash Filename: param.bin
FOTA Filename:

--- Entry #13 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 10
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 124928
Partition Block Count: 65536
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: BOOT
Flash Filename: boot.img
FOTA Filename:

--- Entry #14 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 11
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 190464
Partition Block Count: 77824
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: RECOVERY
Flash Filename: recovery.img
FOTA Filename:

--- Entry #15 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 12
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 268288
Partition Block Count: 16384
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: OTA
Flash Filename: -
FOTA Filename:

--- Entry #16 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 13
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 284672
Partition Block Count: 8192
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: CDMA-RADIO
Flash Filename: modem_cdma.bin
FOTA Filename:

--- Entry #17 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 14
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 292864
Partition Block Count: 180224
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: RADIO
Flash Filename: modem.bin
FOTA Filename:

--- Entry #18 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 15
Attributes: 5 (Read/Write)
Update Attributes: 5 (FOTA)
Partition Block Size/Offset: 473088
Partition Block Count: 2048
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: TOMBSTONES
Flash Filename: tombstones.img
FOTA Filename:

--- Entry #19 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 16
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 475136
Partition Block Count: 2048
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: DNT
Flash Filename: dnt.ssw
FOTA Filename:

--- Entry #20 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 17
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 477184
Partition Block Count: 1024
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: PERSISTENT
Flash Filename:
FOTA Filename:

--- Entry #21 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 18
Attributes: 5 (Read/Write)
Update Attributes: 5 (FOTA)
Partition Block Size/Offset: 478208
Partition Block Count: 24576
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: PERSDATA
Flash Filename: persdata.img
FOTA Filename:

--- Entry #22 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 19
Attributes: 5 (Read/Write)
Update Attributes: 1 (FOTA)
Partition Block Size/Offset: 502784
Partition Block Count: 5120
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: RESERVED2
Flash Filename: -
FOTA Filename:

--- Entry #23 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 20
Attributes: 5 (Read/Write)
Update Attributes: 5 (FOTA)
Partition Block Size/Offset: 507904
Partition Block Count: 6144000
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: SYSTEM
Flash Filename: system.img
FOTA Filename:

--- Entry #24 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 21
Attributes: 5 (Read/Write)
Update Attributes: 5 (FOTA)
Partition Block Size/Offset: 6651904
Partition Block Count: 409600
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: CACHE
Flash Filename: cache.img
FOTA Filename:

--- Entry #25 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 22
Attributes: 5 (Read/Write)
Update Attributes: 5 (FOTA)
Partition Block Size/Offset: 7061504
Partition Block Count: 81920
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: HIDDEN
Flash Filename: hidden.img
FOTA Filename:

--- Entry #26 ---
Binary Type: 0 (AP)
Device Type: 2 (MMC)
Identifier: 23
Attributes: 5 (Read/Write)
Update Attributes: 5 (FOTA)
Partition Block Size/Offset: 7143424
Partition Block Count: 0
File Offset (Obsolete): 0
File Size (Obsolete): 0
Partition Name: USERDATA
Flash Filename: userdata.img
FOTA Filename: remained

Ending session...
Rebooting device...
Releasing device interface...

Any more kind help, please? Many thanks again.