KTM 990SMT would be top of my list
Also worthy of consideration…
Aprilia Tuono
Aprilia Falco
Ducati Multistrada
Yamaha Tracer 900
Honda VFR800
Tuono will be a laugh a minute and you can tour on one, but not the most practical. Falco’s are ace bikes, and you’ll get £3k change from your £5k budget even for a mint one cos they’re old and unfashionable now, but still worth considering. Multistradas are cool, but belt changes and general Ducati running costs put me off, and air cooled motors not that powerful. Tracer 900 seems like a great bike, just too new to get under £6k for now, but would probably tick all the boxes. VFR800’s are more sports than tourer despite what the race rep boys would have you think, but I’m not a fan of the later VTEC engines, the older 98-02 model is fantastic but will undoubtedly need some money spending on age related upkeep, you could look for early 2014 models with a few miles in, starting to come down to near your £5k budget and is a much newer bike (and the VTEC is toned down hugely too).
But I’d probably buy the KTM990SMT out of those if you can only spend your budget on one bike and you need fun and touring capabilities. I only need the fun bit, so recently traded my fantastic 99 model VFR800 in against an 08 Aprilia RSV1000R! 😆