Help determining square steel tubing size for a gate

The steel solves the sagging problem... The next problem will be the post.... Just a 5' gate... The post will probably be fine... House I sold a few years back I'd built a 14' gate out of 1.5" x 095 tube hung off a 3.5" steel post that was connected to a second 3.5" steel post by a pair of 1.5 x .095 tubes.. I could stand on the outboard end of that gate & it wouldn't sag at all...

For a 5' gate .065 wall 1.5" tube would be fine....