The DSP5500, 6000 and 7000 all share the same internal electronics, so sound differences are down to cabinets and firmware.

In my experience, the bass of the DSP5500s can be very difficult to control - if your room isn't sympathetic, then the bass can be overblown and over-powering.

The DSP6000s for me work in all the environments I've tried them in. In my house system, they are currently either side of a fireplace without a lot of room but still sound excellent.

A friend used to run DSP7000s and swore by them as he has a very strange room that seems to suck bass away. He's tried lots of different speakers (both DSP and passive) and has always come back to Meridian DSPs.
DSP6000s didn't work as well as the DSP7000s in his room.

If you can find a decent pair of DSP6000s they won't disappoint! Get them re-capped to allow them to really sing...

Good luck,

Steve

Main: 861v6 (LPS), 808v6, UHD722, DSP8000SE Anniversaries, DSP5200.2HC, DSP7200.2, SW1600, Sky Q, Cambridge Audio BD, Roon, M80
Office: 861v4 (LPS), 818v3, 800v4, HD621, M&K S150P, DSP5500HC, M&K MPS2810 sub x2
Son's system: 861v4, HD621, DSP6000.2, DSP5200HC, DSP33
Spare: MCD, 100 Series, 200 Series, 500 Series, F80s, C15s.