I've made a quick test where I put 12V from a dc power supply to a 15V regulator - so the "input" was lower than the voltage regulator output.
When I measured it, I had a 5V output, and it was what I'm looking for intially, and the regulator wasn't hot.
So I would like to refer to your expertise and ask you if it is a good way to get 5V without any issue like a current drop for example, which is crucial for the working of my components?