Impedance matching an RLC circuit (inductor macroscopically drawn on PCB)
Oh no, I'm a physicist too.  (I hope I can still help.)
So I'm going to guess that both your numbers are correct.
The Q of a resonant circuit can certainly change as you load it down with more power.
(Is there something in those coils?)
There will also be some resistive loss in the matching network.
When imputing power at RF you need to know something about the source impedance. (What's driving it?)  And then maybe something about the connection (transmission line) between the source and the load.  5 MHz, is fairly low freq, RF-wise, how long is the connection?