I think you misread him having an i5 processor in his iMac, instead of an iPhone 5
A Mac Mini is fine. It should work with your flat screen TV as a monitor or any good computer monitor. You will also need a keyboard and or mouse trackpad.
Setting up the Mini with your flat screen TV should be easy depending on the TV inputs. Most everyone uses HDMI nowadays, so yes, that's good. You will of course need to purchase an adapter or cable to run from the Mini to the TV.