Pip - quick and dirty response:

A 5th above B is F#, not F - just to start off...

You can run a parallel 5th to any melody line you like - or parallel 4ths, or parallel 3es, etc. The question is whether these parallel lines fit the underlying harmonic structure of the melody.

So, for example, if the first 3 notes of Three Blind Mice in the key of C are E, D C, then you could have an underlying chord structure to those notes of C, G7, C - and you could also play a 5th above with notes G, F and E. Note that the G7 chord includes the F note. In this the parallel 5th above suits the tune

However, if the underlying structure of a tune is not straightforward, an unthinking, standard parallel 5th might not suit. All harmony is, of course, in the ear of the listener, but music convention might subdue creative impulse!