I have virtually no Betamax experience but lots with VHS and to me this sounds like there is no FM video signal being fed to the heads in record mode.
What test equipment do you have? a scope would be ideal. I can't find a manual for the SL-5000 but if it is a close relative to the SL-C6 as Fivos suggests then looking at the manual for that model there are several fusible resistors that could possibly cause this fault, these could be checked with just a multimeter. The manual for the SL-C6 can be downloaded
here
John.