Gm7b5/F (G Half-Diminished 7th over F)

A slash chord names two things at once. The part before the slash is the chord your right hand plays, and the part after it is the single bass note for your left hand. Read Gm7b5/F as G Half-Diminished 7th with F in the bass.

The bass note here is one of the chord tones, so this is exactly the 3rd inversion of G Half-Diminished 7th, written the way sheet music and chord charts usually write it.