Are there any five nines hosted database services?

Er, yes, but I'm not sure if this will be a satisfying answer:

If you contact IBM Global Services, they have a group that can put together a hosted database proposal with very stringent uptime guarantees. Most likely they'll push for you to be hosted on z10 (mainframe) architectures and DB2. They can run it across a multi-site SYSPLEX in multiple tightly controlled data centers. They've got a handful of customers who have been continuously up since at least the late 1980s in a config like this.

This topic came up at OpsU in SF a couple weeks ago. I think the consensus from all was that looking for "five-9s" is a very bad proxy for asking the question, "What is the cost-benefit of downtime mitigation strategies?" I've worked on systems that required (either because of regulation or health and safety) appreciably 100% uptime. The cost for near-perfect uptime almost never balances against the cost of downtime including lost revenue, lost customer confidence and the like.

Now, one of those applications did happen to be a telecom application (a switch), and there was, before deregulation, a universally accepted requirement that billing records must continuously capture 99.999% of the time. No clue if that still exists, but if that's you, there are about a kajillion preexisting solutions to this problem, and many of them are hosted.

The Magic 8-Ball says: Concentrate harder and ask again. :-)

Better question is: Is there any hosted anything that actually delivers five 9's?

Most SLAs are crap. Yay, you get a credit of $50 for our 8 hours of downtime. If you're building a mission critical service based on Some 3rd party SLA, you're in for a world of hurt.