Indeed : radio transmissions follow Friis equation [1] -- power decreases by the square of the frequency (same goes for distance). So, going from 2.4 to 5 GHz cuts the received power at a certain distance by a factor of 2 (more or less). Assuming free space, of course : obstacles will make matters worse, depending on frequency, thickness and materials.

Meaning that going from 5 GHz to 6 GHz will decrease the range by a factor of around 1.2

[1] https://en.wikipedia.org/wiki/Friis_transmission_equation