Slash chord, „m7b5 over [b5]”. On the left side of the slash you can see a chord, on the right side the lowest tone (bass).
The m7b5 chord consists of the tones  (1), [m3] (m3), [b5] (b5) and  (7). As you can see, the bass [b5] is part of the basic triad of the chord. The bass on the right of the slash does not necessarily be part of the chord symbol on the left, except the bass is part of the basic triad. In this case it wouldn't make any difference, since even without the flat 5th, the chord on the left would be written as m7b5.
You can find the m7b5/[b5] chord in the same situations where a [b6]7/[b5] (=[b6]/[b5]) could be written respectively played. Let me explain: you can nearly always add a 9th to a dominant 7th chord. By moving the root of the [b6]7/[b5] two frets up to , you end up with the same chord shape as the m7b5/[b5] chord. Thus, you may interpret the m7b5/[b5] chord as [b6]9/[b5] that is played without its root [b6].
[m3]m6/[b5]: the m7b5 chord consists of the same tones as a [m3]m6 chord. Thus, the m7b5/[b5] can also be seen as [m3]m6/[b5] chord. In fact, you can play/write the m7b5/[b5] in the same harmonic context where a [m3]m6 might be played/written. To make it even easier, you can see the , the 6th of the [m3]m6, as just a melody tone and write the m7b5/[b5] as [m3]m/[b5].