There is a supposedly very nice transit hotel built into the airside of the Sheik Rasheed Terminal (the airside part of DXB). Not sure on prices, but you should be able to get information on the DXB website.

I did not find Dubai Duty Free to be all that exciting (or different from any other Duty Free facility). Definately not enough to keep you occupied for five hours. Also, the BA lounge is not all that special. Just a standard Terraces lounge with no First Class section. No showers, either.

Dubai is an interesting place and well worth a visit of more than five hours. With five hours, you shoudl be able to get a glimpse of the city. Immigration lines can be long. I would estimate an hour to get landside (a very conservative estimate, I'll add). You should plan to be back at DXB no later than 90 minutes prior to your flight (security is understandibly tight). That leaves you with about 2.5 hours to explore the city. With that time, I would take a taxi to the Spice Souk and walk around the Deira side of the Creek. You see the Spice and Gold Souks, the dhows unloading at Dubai Creek, the skyline (including the Burj al-Arab) and get a sense of life in Dubai.

Will you be doing this at night, connecting to the 2 AM BA flight?