No Output From LM2596-5T from TI. Any Ideas Why?
Your inductor is connected wrong. You should have wired it up to pins 1 and 3 (diagonally opposite):



As a result the inductor is basically on open circuit, so you will get no output.

Given your VCC trace passes right next to pin 3, you should be able to simply scape off any soldermask from the trace where it passes the inductor pin, and make the connection with a blob of solder.