Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 170; Flight Crew Total 8700; Flight Crew Type 490
Situational Awareness
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance
Human Factors
We were cleared to [destination] via the CLRBK2 departure to J534 to IWACK intersection; after departing we climb up to 5;000 ft and ATC told us we were close to terrain and they ask us to climb; we complied with ATC. We understood climb via the Sid to intercept J534. At no time were we in danger it was a VFR day; clear and no terrain warning called out on the cockpit. We had the terrain in sight at all times at it was below us at all times.
Departure called and told us to climb; and asked if we had the terrain in sight. We complied with the climb and had the terrain in sight at all times. We were informed that we should have flown the SID and waited for vectors to the airway. Since vectors were not included in the clearance; we did not expect them. We misunderstood and should have asked for clarification. We do not feel we were in danger but ATC did. Next time; we ask.
Air Taxi flight crew reported ATC issued a low altitude alert departing CYXX.