Ok. Did you build the amp, and will you be performing the troubleshooting yourself?
Given that pin 5 was within reasonable ranges and matching that narrows the possibilities to:
Two consecutive sets of tubes with a short in one of them that were coincidentally in the same socket. (Unlikely, but not out of the realm of possibility).
A failing coupling cap from the PI that leaks slowly and/or only under load and/or heat.
If you're performing the troubleshooting I'd recommend lifting the coupling cap that feeds V5 (lift the leg on the negative voltage side) and temporarily adding a 1M resistor to ground. Measure the voltage across this added resistor. It should be very near 0. Let the amp run for a few mins and monitor that voltage. If no change, apply heat with a heat gun or blow dryer and monitor.
If no change, then reattach the cap and reinstall the tubes. If you have a lightbulb limiter hook it up and power the amp on while monitoring the voltage at pin 5. Preferably on both tubes, but if you only have one meter put the probes on pin 5 of both tubes. The difference should ideally be 0v. If at any point it deviates by 3v or more shut the amp off. This will confirm bias runaway due to a leaking cap. The sign (positive or negative deviation) will tell you which side was beginning to runaway if you keep track of which probe was attached to which tube, but I'd replace both with at least 400v rated replacements, 630v preferable.