My J's Mooney Service Manual specifies a MIL-L-3545 (High Temperature) grease for the wheel bearings which is satisfied by the use of AeroShell 5. Aeroshell 6 on the other hand is an appropriate airframe grease in some applications.
While AeroShell 22 appears to be an excellent wheel bearing grease it's not what's specified for my J. I doubt anyone would care if you used it though.
Here are the specs for AS-5 directly from Shell:
AeroShell Grease 5 is particularly effective for use as a wheel bearing grease, especially when landing speeds are high, and is suitable for the lubrication of aircraft and engine accessories operating at high speeds and at relatively high temperatures, e.g. magnetos, generators and starters. For the lubrication of rolling bearings which are required to start at temperatures as low as –23°C an adequate period should be allowed for the grease to channel. SPECIFICATIONS PROPERTIES MIL-G-3545C TYPICAL Oil type - Mineral Thickener type - Microgel Base oil viscosity mm²/s @ 40°C - 500 to 525 @ 100°C - 32 Useful operating temperature range °C - –23°C to +177 Drop point °C 177 min 260+ Worked penetration @ 25°C 250 to 300 284 Unworked penetration @ 25°C - 281 Bomb oxidation pressure drop @ 99°C 100 hrs lb/in² 10 max 6 500 hrs lb/in² 25 max 15 Oil separation @ 100°C, in 30 hrs %m 5 max 0.5 Water resistance test loss @ 41°C %m 20 max 0.5 Evaporation loss in 22 hrs @ 149°C %m - 1.0 Mean Hertz Load kg - 37 Copper corrosion 24 hrs @ 100°C Must pass Passes Bearing protection 2 days @ 51°C Must pass Passes Anti-friction bearing performance @ 149°C hrs - 600+ Colour - Amber AEROSHELL GREASE 5 U.S. Meets MIL-G-3545C (Obsolete)
Agree, AeroShell grease 5 is the correct grease for wheel bearings. After reading the specs and talking with my IA this is what I have used since I bought the airplane. I went through this effort years ago when I tried to put together a good list of consumables for my annual inspection.