G550 Captain reported encountering wake turbulence descending through FL380 13 miles in trail of a B787. Reporter suggested increased separation might be advisable.

Narrative

Re: Enroute wake turbulence encounter. We were proceeding to LAX via the ANJLL 4 RNAV ARRIVAL in the vicinity of the SHTNR intersection at FL400 and Mach .83. ATC assigned an initial descent; but we were not yet cleared to 'Descend Via' the RNAV arrival. Descending through approximately FL380 we encountered what felt like the start of light chop. When it was evident it was likely a wake encounter; the pilot flying (PF) disconnected the Autopilot and shallowed the descent rate in the attempt to get out of the wake zone. The aircraft suddenly rolled into an approximately 40 degree angle left bank. The PF returned to level flight and further shallowed the descent rate. We did not experience any other encounters for the remainder of the flight. We queried ATC as to what type aircraft we were following and were told we were 13 miles in-trail of a B787; also descending.The seatbelt sign was turned ON at the top-of-descent. However; one pax was not in their seat at the time of the encounter. The flight attendant and the PIC checked the cabin and spoke with passengers; and confirmed there were no injuries or damage in the cabin. The encounter did not lead to any RVSM excursions or aircraft exceedances.Suggestions: Although we were 13 miles in-trail of the B787 we still encountered significant wake turbulence. Although at the time I did not know what type aircraft we were following; I don't know that I would have been concerned if ATC had told me it was a B787; due to us being at least 13nm behind him. Perhaps a re-evaluation of safe in-trail distances is in order. One contributing factor is that we were executing an ATC descent clearance; not a 'Descend Via' clearance. I don't know what type descent the B787 was on; but it seems more likely that if we would have both been on a Descend Via clearance the risk of us descending below his wake profile would have been less likely.