voltage regulator current draw
You're using a linear regulator which simply "burns off" the excess voltage.

The current does not change and remains the same so you can draw up to 1.25 A at the output of the regulator. So after the regulator you're limited to 5 V, 1.25 A so 6.25 W.

When you draw that 6.25 W there is 12 V - 5 V = 7 V at 1.25 A meaning 7 V * 1.25 A = 8.75 W dissipated in the regulator. It will get hot so use a heatsink! Note how 8.75 W + 6.25 W = 15 W which is the maximum power from the supply.

If you want more current at 5 V you will need to use a switched mode regulator (also called a "buck converter"). Then theoretically you could draw up to 15 W at the output so 5 V, 3 A. I write theoretically because this assumes no power is lost. In practice some power is lost and 5 V, 2.5 A would be a more realistic value. An LM2596 based DCDC converter board could do this job.