VGA absolutely can be used for 120 Hz, VGA has no limit on refresh frequency. Can VGA run 144Hz? VGA (Video Graphics Array) or D-Sub is an old analog connector

For viewing distance of 5ft, 32″ with 1366×768 should be fine. What resolution do I need for 32-inch TV? Another consideration we did not discuss in the above article is

The HowToAV team gives a definitive guide to audio visual signal transmission distances using the various AV cable formats.How far will an AV signal transmit? Signal / Cable Type Resolution