I have not found the documentation for the 5004, but the one for the 5005 is available here:
http://ftb.ko4bb.com/manuals/198.21.21.21/Racal_5005-5006_Digital_Multimeter_Service_Manual_1981.pdfFortunately the 5004 share apparently a lot with the 5005.
I think it will be good enough for a start.
After a quick check I found a missing component in the voltage reference area.
Originally component (AR3) was a AD542.
I replaced it with a LF536. After this operation the multimeter was not giving more signs of life.

I check the temperature on thee ICs close to the OPA I replace and I almost burned my finger on U11.
Apparently the dumb ass who did some repairs on this unit did install U11 in the wrong way . After a closer check, same for U10.

Figers crossed, I turned the unit on .... magic it works again, or at least it's displaying something and oing a boot sequence.