Hetman Nr. 6 Heavy Slide oil, a heavier-viscosity synthetic lubricant for looser-fitting valve slides and for calve slides of shorter length, improves slide tube seal, prevents binding when making intonation adjustments, protects against corrosion and wear, 30 ml
I bought this for my girlfriend's house (already owning the no.5 I went for the 6 for variety). For tuning slides it worked great, and was plenty fast enough.
If choosing between the 5, 5.5 and 6 I would get the 6 because it is plenty fast enough and being a bit thicker means that it will stay put for longer and potentially have other uses (such as keys and spindles on a rotary instrument).