[Galaxy S 4 Active General] phase_shyfter:
The original version of the guide as well as all relevant files can be found here:

deathonater.wordpress.com/2015/05/22/rooting-the-samsung-galaxy-s4-active-gt-i9295-with-android-5-0-1-lollipop/

I created this after fruitlessly scouring the xda forums for a comprehensive and easy-to-understand guide to rooting the I9295 with Lollipop. I am a fairly new user with few posts, so I am not yet allowed to post links. I hope my experience can be of use to anyone trying to root their S4 Active with Lollipop. Please let me know if there are any errors.

If you would like to root a Galaxy S4 Active with Android 5.0.1, or you have upgraded a previously rooted Galaxy S4 Active to Android 5.0.1, and discovered that the upgrade process unroots the device, follow the steps below to (re)acquire root access:

POINTS TO NOTE BEFORE ATTEMPTING THIS PROCESS:

Read this guide from beginning to end and understand the process before doing anything.

This guide is intended ONLY for the I9295 version of the Galaxy S4 Active, I have not tested it with the AT&T version, or any other phones.

This will flag your operating system as modified, meaning you will not be able to update the OS from the Software updates menu item in Settings.

Please be aware of the risks involved with flashing and rooting phones. I am not responsible for any damage done any device modified using this guide.

Files you will need (available at the URL above):

Odin

CWM

SuperSU

Step 1: Extract Odin, and CWM.

Step 2: Do NOT extract the SuperSU file, just copy it to the phone (NOT the phone’s SD card) and make a note of where it is located.

I suggest downloading the file using the phone’s browser, so that it will be saved to the downloads folder.

Step 3: Power off the phone (do NOT reboot, shut down the phone completely).

The phone should NOT be plugged in to a PC.

Step 4: Boot into download mode by holding down the Volume Down and Power buttons at the same time, then press the Volume Up button only when prompted.

Step 5: Start Odin.

Be sure Auto Reboot and F. Reset Time are both checked.

Step 6: Click on the AP button and select the CWM file ending with the .md5 extension.

Step 7: Connect the phone to the PC.

Step 8: Hold the phone in your hand and be prepared to hold down the Volume Up and Power buttons the moment the phone reboots. Do NOT allow the phone to boot fully after flashing CWM, you must boot into recovery right after the flashing process is complete, or else you will have to start over.

Step 9: Click on the Start button in Odin to begin flashing CWM.

Step 10: As soon as the flashing process is completed, the phone will reboot, quickly hold down the Volume Up and Power buttons, and the phone should boot into CWM Recovery.

CWM recovery will have a gray background and the ClockWorkMod graphic will be visible. If you see a black background with orange text, or anything other than what is described, that is not CWM, you will need to start over.

Step 11: Using the hardware buttons, select the option to install zip from phone.

Step 12: Navigate to where you saved the SuperSU file and install it, the phone should reboot.

Congratulations, the Galaxy S4 Active should now be rooted!