5VDC and 10VAC on the same PCB - what happens on 10V goes to 5V ground?
Well it depends, but just about every device running off a floating (rather than earthed) DC power supply already has both of its power input potentials relative to earth oscillating at mains frequency and at a good portion of mains voltage, merely staying at a fixed potential relative to each other - and obviously these devices are still operational. Designing a device that is too sensitive to mains frequency interference will make it generally inoperable in normal household conditions. If the device was operational before, you should expect it to be operational after you short one of the floating AC lines to DC.

The oscillating potential is not measurable, as the moment you connect your voltmeter between the power supply outputs and the earth, the voltmeter resistance of maybe 10 or 20 MOhm will pull the potential in question to ground.

It's a bit more difficult to predict what will happen due to higher frequency AC. Some common mode noise current may be induced, but again this is always something to contend with, and fundamentally same as proximity with no short. The DC power supply actively drives one of the outputs with low impedance to maintain a fixed voltage.