Cessna Stationair/Turbo Stationair 7/8
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Communication Breakdown
ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Flight Crew Overcame Equipment Problem; Flight Crew Returned To Clearance
Human Factors
I was vectored while arriving the ZZZ terminal area. I  was established on V-XXX at 6000 feet MSL. I was instructed to fly a 240 degrees heading and to maintain 4;000 feet MSL. I read back 'Heading 240 maintain 4;000 feet.' Air Traffic Control did not correct my read back. I received a new heading of 220. Once reaching 4;560 feet MSL; ATC advised me of low altitude alert and to maintain 5;000 feet MSL. ATC said I was assigned 5;000 feet MSL. I was then vectored to join the final approach course for the Runway XX. The flight was completed without any more issue. No Brasher was issued.Air Traffic Controller assigned me 4;000 feet MSL. I clearly read back 4;000 feet MSL and ATC did not correct my read-back.
Small Transport pilot reported a communications breakdown between fight crew and ATC during approach descent. ATC mistakenly assigned 4;000 feet instead of 5;000 feet. Flight crew issued and complied with a climb clearance and completed flight with no further issues.