The JP5 entered service as the T Mk 5. In 1974, the avionic upgrade programme for the JP3 and JP5 began; out went the prehistoric Eureka DME receiver, single UHF and the excellent G4 compass and in came a VOR-ILS, civil DME, CL6 compass and an extra VHF radio (I think?); this was the -A upgrade.
All remaining JP3s and JP5s were converted to 3A and 5A standard. No such modification was ever carried out on the JP4.
The JPs at Finningley (for half-wing half-brain training), with extra tip tanks, no moustache fairings and no concrete wing leading edges then became JP5s.
There was NEVER an 'official' Jet Provost T Mk 5B. It's a spotter's myth (as is 'Phantom F3' for the Phantom F4J(UK)).
One wacky idea for ME training was to include an exhaust deflector and twin 'throttles' in the JP, so that single engine failure could be simulated with reduced performance and a substantial yaw moment. Fortunately this barking mad idea never flew....
And ALL Jet Provosts had the horn balanced rudder! Even the original T Mk 1.