G550 Captain reported a wake turbulence encounter contributed to an altitude overshoot departing MCO in trail of a B757.

Narrative

Departure out of MCO called for the first restriction at or below 5;000 ft. I elected to select VNAV as the Pilot Flying (PF) for the departure mode. After a runway change; we delayed departure for wake turbulence avoidance from a departed 757 ahead of us; which I believe caused the ride to be a little bumpier than it would have otherwise been. On climb out; our vertical speed had reached a high rate (> 3;000 fpm? But probably much higher); and as I was in the right turn off of runway I heard the VNAV altitude alert chime; I looked down at the VSD; which I quickly noticed (remembered) had the BELOW 5;000 on it. I queried the Pilot Monitoring (PM) if that first altitude was below 5;000 ft.; and the PM didn't respond. At this point I believe we were going through > 4;000 ft. with a very fast rate of closure on the altitude restriction. I said aloud; 'It's 5;000. I'm going to level'; at which point I started applying forward pressure on the yoke to level off. I didn't want to unload the airplane abruptly; so I ended up leveling off around 100-150 ft. high; and slowly corrected back down to 5;000 ft.; and made the below restriction at the waypoint; as required.I could have prepared for this altitude restriction better by using the Vertical Speed mode instead of VNAV (VFLCH) and setting the altitude selector to 5;000 ft.; then changing the altitude selector after passing the restricted waypoint; which would have given me much more precise control over the rate of ascent & level off. Specifically calling out any 'BELOW' restrictions and a plan to meet it would have made a better briefing.Contributing factors were - The G550 has very high climb performance; especially when light. We were a relatively light weight that day; at sea level. We were quick turning. Although we didn't rush and thoroughly briefed; we may have had more time to 'think about it' and elected to brief the alternate procedure of using VS instead of VFLCH on departure. Contributing to this was increased crew focus on the runway change during taxi and wake turbulence avoidance; plus the updrafts during climb out. The PM is relatively new to the aircraft; which may have contributed to task saturation after departure; decreasing the SA (Situational Awareness) as well.