C560 flight crew reported encountering wake turbulence climbing through 5;000 ft in trail of a regional jet that resulted in an abrupt change in roll and pitch causing a 0.3nm lateral course deviation with a pilot deviation warning from ATC.

Narrative

Airport: BOS - Logan Int'l AirportRoute: BOS-ZZZRunway: 22RSID: SSOXS6 RNAV DEPARTURETAKEOFF RUNWAY 22R: Climb on heading 215 degrees to intercept course 144 degrees to TJAYY do not exceed 210K until 520 ft. MSL; thence on depicted route to SSOXS. Maintain 5000 [ft]. Expect clearance to filed altitude/flight level within ten (10) minutes after departure.At XA:33:23 the ATC cleared for takeoff Aircraft Y; immediately clear Aircraft X to line up and wait on Runway 22R. 1 minute 23 seconds later; Boston Tower clear for takeoff Aircraft X from Runway 22R. On the initial climb; Aircraft X maintained the present heading which is the runway heading 215 degrees at 1000 ft. the Autopilot was engage confirmed with the FMA (Flight Mode Annunciator) with LNAV AND FLC (FLIGHT LEVEL CHANGE) modes climbing via SSOXS6 at the moment 5;000 ft.In the first call with Departure Control at XA:36:06 the Pilot Monitoring (PM) confirmed climbing via the SSOXS6 Departure and the Departure Controller give climb and maintain 14;000 ft. clearance; the moment of the left turn the wake turbulence caused by the Aircraft Y enroute to ZZZ1 provoke an unexpected roll and pitch which cause Autopilot disengagement; in this moment pilot flying (PF) take immediately control of the aircraft but causing a 0.3 nm deviation from the lateral path of the RNAV SID; This RNAV Departure is a Class RNAV 1 which comprehend 1 nm left and right deviation. The NPS (Navigation Performance Scales) never turn amber or any alert to the crew that they deviate from the SID so they control the aircraft and continue flying the Departure. The Departure Controller start giving vectors to the crew and on Boston Control the crew was informed of a possible pilot deviation.If the lateral deviation was 0.3 nm to ft. (1822 ft.); the RNAV 1 tolerances take in count this lateral deviation without any penalty for deviation. In conclusion possible cause was the lack of situational awareness both pilots and Tower Controller to cleared for takeoff an aircraft without the recommended time separation / wake turbulence caution call and the pilot accepting the takeoff clearance as well not informing the ATC of this situation.