When a tab has a slide like /5 etc. how do you go about starting? Obviously with slides like 3/5 and 5/3 you slide from the former to the latter, but when there is only one fret given in a slide how do you start? I've just been hammering on to the 5th fret for lack of knowing this? does it even mean slide?
For the non-descript slides like that, it's not really that important. I'd recommend listening to the original, but someone will use that notation if they're just sliding into that note from where ever they happened to have their hand. Or, they might start arbitrarily lower on the neck and just slide up. But they didn't really hit a distinct note and linger there long enough for the tabber to want to specify the starting position (I recall this frustration myself at one point).

I'm sure you're looking for a better rule. But I'd recommend just picking somewhere nearby and sliding instantly into the destination note (so that the rhythm beat is right on that note) and don't spend noticeable time on the starting note. That will sound better than a hammer on. And listen to the original if you have it to see how the original did it.
Yeah it just means "slide in from below". From where isn't specified so you'd typically want to lightly pick a random note (in key is best) and then quickly slide up to 5.