I've had the phone for two weeks and so far I'm completely satisfied.
When it arrived, it came in perfect condition - I would have thought it was new - and the set up process was completely normal for an Android phone.
The phone works as expected, no nasty surprises so far, though it is still early days.
I was very happy with the ordering process, and really pleased that I got this model of phone, which is increasingly difficult to find (plus it's really sad Sony isn't continuing the 5 series at all), and pleased that I got it for a decent price. I can see myself ordering my next phone through Back Market, provided that this one holds up.