Every fingering that fits a hand
x556
moderate · barre · no 5
acbc
hard
a9bx
easy · no 5
a9b8
hard · no 5
a9bc
hard · no 5
What is true of it
F7 is F, A, C and E♭ — 1, 3, 5 and b7 counted from F.
On an instrument that cannot reach all 4, the 5 goes first, in that order.
The easiest of the 5 fingerings below is x556: 2 fingers, one of them barring the 5th fret, 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 of the 5 need a barre.
It leaves out the 5. 4 strings cannot carry 4 notes, and the 5 is the one this chord can lose without changing what it is.
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
F7/A
2310
F7/C
5556
F7/E♭
x310
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.