Uh, no.
Provding 10 amps at 120 volts, the line voltage, completely neglecting conversion losses, requires 100 amps at 12 volts, a typical UPS battery voltage.
Five minutes is 1/12 of an hour.
100 amps x 1/12 of an hour =~ 8 ampere-hours
A 1500VA UPS having an 8.5 ah battery is just a tick under $200 at Walmart.com. You might want a somewhat larger one, which costs more, but nowhere near what your labor will cost to roll your own.
Did I mention that when your prototype circuit turns out to be not exactly right, as they all do, all that will remain is a pile of smoking, burned, possibly still burning, useless junk that used to be expensive components? Experimenting with power electronics gets really expensive really fast, even if you don't get hurt.
Buy a UPS. How big and expensive depends partly on the holdup time you need, and partly on how well your load will tolerate nonideal waveforms.
Mike Halloran
Pembroke Pines, FL, USA