LM2596 Voltage Regulation Problem
The fact you always get 1.25V sounds suspicious to me. This is often the Vref voltage for adjustable regulators. Checking the datasheet for the LM2596 says it's 1.25V also.  

Are you sure you don't have the adjustable version?  

One way of finding out easily is to set up your circuit as if it was and see if it works. 
Add the two resistors in the diagram below - R1 should be 1k and R2 3k for 5V.
The feedforward capacitor across R2 (Cff) shouldn't be necessary with this setup, but you can check TI's better datasheet for info on selecting one for situation when it is necessary (over 10V out or extra low ESR on output)