A Corporate Jet Captain reported departing LAS Runway 19R behind a B737 which departed Runway 19L. During the climb out the Jet entered the B737's wake turbulence and was vectored by ATC.

Narrative

We were told to maintain visual separation from a B737 departing from Runway 19L when given our takeoff clearance from Runway 19R. The winds were light. We maintained approximately 4.5-5 miles in trail as our paths converged between JAKER and ROPPR Intersections on the COWBY Two Departure. About 4 miles prior to ROPPR; we encountered what was most likely the B737's wingtip vortices resulting in fairly rapid excursions of 2-3 degrees of pitch and 5-10 degrees of roll. Within 10 seconds of this; we requested a climb from LAS Departure advising them of the encounter with B737's 'wash.' We were given a turn and a climb while the B737 also leveled off; so we exited the wash. Suggestions: We could have told Tower that we wanted 30 seconds of separation. We were not able to climb much faster as we were fairly heavy. LAS Departure could have given an early vector to either us or the B737 or had the B737 slow their climb. Even 10 seconds of extra separation before giving us our takeoff clearance might have avoided the event.