Why are incandescent bulbs blowing/burning out? How to prevent?

If the string is working with 120V, pull-out one lamp. All of the bulbs in series will go out. If any stay-on they are in a separate series-string.

If you have a series string of 50, that's 120V/50 = 2.4V per bulb. The energy/wattage from 120V RMS is the same as 120VDC. (Don't worry about the peak AC voltage.)

So with 5VDC, two in series would be slightly over-voltage but probably OK.