Date: 202011
Local time of day: 1801-2400
Location: ZZZ.TRACON, US
Flight conditions: VMC
Light: Night
Aircraft: Regional Jet 900 (CRJ900)
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class E ZZZ
ATC / advisory: TRACON ZZZ
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness; Communication Breakdown
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance
Contributing factors: Human Factors; Procedure
Primary problem: Human Factors

Narrative: We had just switched on to approach frequency and were given a heading and altitude for the visual approach. We both heard the altitude clearance as 5;000 ft. and the PM read back 5;000 ft. A few min after we had leveled off at 5;000 ft. ATC asked us to confirm altitude and gave us the altimeter. We responded with 5;000 ft. and verified we had the correct altimeter. ATC then responded the minimum vectoring altitude was 5;300 ft. for that area. As the PM (Pilot Monitoring) attempted to clarify we read back 5000 ft. in the initial clearance; I started a climb to 5;300 ft. ATC then asked if we had the field in sight which we did and then we were cleared for the visual approach using the GPS 14 approach plate as guidance. We landed normally.The cause of this event was a miscommunication with ATC. We both heard 5;000 ft. in the initial clearance not 5;300 ft. The PM read back 5;000 ft. and we didn't hear a correction from ATC. A contributing factor in my opinion was the fact that we were experiencing light to occasional moderate turbulence for most of the flight including the descent and that could have caused us to miss hear the original clearance and potentially the read back was hard for ATC to hear due to the PM's mic being jostled.In cases such as this we could have requested clarification if the altitude didn't sound correct but in my estimation the clearance seemed to make sense based on our position and the airport elevation and the location of obstacles and terrain which were not a factor from the direction we were arriving and they also seemed to be similar to the altitudes we would expect if on the GPS approach we were using as a backup. But it would be prudent in the future especially in turbulence to verify clearances considering the effect turbulence could have on radio transmissions.


Second narrative: We had just checked in with approach and they gave use a heading to turn to for vectors and an altitude to descend to. I thought I had remembered reading backing 5;000 ft. as the captain who was the PF put 5;000 ft. in the FMA and we both confirmed the 5;000 ft. once set. After reaching 5;000 ft. the controller asked us to verify our altitude and I read back 5;000 ft. The controlled returned with 'the MDA is 5;300 in that sector do you have the field in sight?' We had the field in sight but the question led us to believe we descended to the wrong altitude. The controller didn't clarify the altitude at this point and said were cleared for the visual using the RNAV GPS 14 approach plate for guidance.The cause of the event was a miscommunication with ATC and I could have possibly read back a different altitude and thought that 5;000 ft. was what he said instead; after we had set 5000 ft. Also; we were in light to moderate turbulence during the entire flight and it might have caused me to mishear the controller or misread the altitude.I should have asked for clarification from the controller after we had set the altitude in the FMA. From where we were; the altitude of 5000 ft. made sense so it did not cue me to ask for clarification. We had briefed the approach plate as well and the higher rising terrain was on the other side of the field and we determined it would not be a factor for the altitude of 5000 ft. Where we were seemed to coincide with the altitudes on the approach plate as well.


Synopsis: CRJ900 flight crew reported descending below minimum altitude for the area due to a misunderstanding of assigned altitude.