The RAF museum holds the following which may help:
AP4576A; Fire crash truck, Mk.5A: General and technical information, repair and reconditioning instructions
AP4397A; Truck, 3 ton, GS, Cargo, 4 x 4, Thornycroft, Nubian, TF/B80: Tractor, 10 ton, GS, 4 x 4, Thornycroft, Nubian, TF/B80: Chassis, 3 ton, GS, 4 x 4, Thornycroft, Nubian, TF/B80: User handbook (this is the Thornycroft manual covering the engine and chassis issued in an AM cover)
Chassis lubrication diagrams
EDIT: sorry, i just realised I missed off an AP!
AP4386B covers the equipment fitted to the Mk5
The Mk.5 and 5A are the same chassis/engine with different bodies and slightly different equipment from what I can tell.