Although it appeared in the 1975 HP Catalog, it does indeed have a processor, though no suitable micros were available at the time. The processor is an all TTL job, with 4x 1K ROMs as instruction decoders and 3 16x4 SRAMs as working store. The processor operates on 16 BCD digit numbers, one decimal digit at a time, rather like a calculator.
The 5345A was a quite revolutionary device at the time, and HP Journal issue 1974-06 is entirely dedicated to it.
5MB scan from HPMUCH better 25MB scan from HPArchive.com- It has one of the first 500MHz ICs (A single flip flop, in a custom variant of ECL called EEL by HP)
- It is HPs first reciprocal counter
- It is part of the original HP-IB lineup, and certainly the centerpiece, with the 9820A calculator
- It uses a clever phase modulation randomizing scheme on the time base to improve accuracy when averaging
- It can take it's own new plugins, or any 5245L plugin through an adapter chassis
- It can measure frequencies to 18GHz through plugins.
- It has a very stable Ovenized time base as standard
Mine is calibrated to a
Standford Research FS725 Rubidium Standard.
It's ridiculously large by 2018 standards, it weighs 50lbs, uses 15 Watts 24/7 for the oven and 120W in operation, it's stupidly loud at 53 dB and it's by far my favourite time piece in the lab.

This is what it looks like with a 5245L plugin and adapter (not mine) :

I have ordered a paper manual, the scanned (faxed?)
manual does ok with text, but the figures and tables are unusable. Should arrive in the next couple weeks.
I will document the repair process in this thread.