Francillon states in his book that: "Kawanishi designed two specialised versions - the N1K5-J Shiden Kai 5 Model 25, armed with two fuselage-mounted 13.2 mm Type 3 machine guns and four wing-mounted 20mm Type 99 cannon. It was powered by a 2,200 h.p. Mitsubishi MK9A eighteen cylinder air-cooled radial, while another high-altitude interceptor version was planned around the Homare 44 with mechanically-driven, three-speed supercharger. A prototype of the N1K5-J was destroyed prior to completion during a Superfortress attack."
Further engine details are given as:
(N1K5-J): Mitsubishi (Ha 43) 11 (MK9A) rated at 2,200 hp for take off, 2,070 hp at 1000m and 1,800 hp at 6000m driving a four blade metal propellor
(Projected version of N1K5): Nakajima Homare 44 eighteen cylinder air cooled radial rated at 2,000 hp for take off, 1,880 hp at 2000m, 1,800 at 8000m driving a four blade metal propellor
It seems neither had a turbocharger fitted.