Design Tips on making a battery powered inverter with 5A output
If you're an electrical engineering student at a university you should know about power, and the laws of thermodynamics. Your batteries will supply 59 Wh, you want 120 V x 5 A = 600 W output. Or more. That's 10 times the input power, and then we're not even talking about conversion efficiency. So, back to the drawing board to rewrite your specifications.