What is true of it
F5 is F and C — 1 and 5 counted from F.
The easiest of the 1 fingering below is x588: 3 fingers, held at the 5th fret.
None of them uses an open string, so this chord moves up the neck unchanged — the same shape 1 fret higher is the chord a semitone above.
1 string stays silent.
Where its notes are on the neck
The brass dots are F, the root. Everything else is a chord tone with its degree printed in it.
With a different note underneath
F5/C
x013
An inversion is the same chord with a different note lowest. The name changes to a slash name because the bass is what a listener hears as the foundation.