You stil didn't identify the native resolution of the TV. Can you post a link to the manufacturer and model of the TV? However, the Radeon HD 5450 should have no problem displaying on the TV although gaming performance may be a little slow especially at 1080p even on those games.
Ok, if it says it's up to 720p then your max resolution is going to be around 1280 X 720. That's probably just fine since your graphics card is fairly weak. You might also be able to use 1366 X 768. Windows should be able to detect the correct graphics mode as soon as you plug in the HDMI cable.