Can I use a canon speedlite with a nikon d5100?

Its a canon 550 ex

Nope. Completely incompatible interface.

I'm a wedding photographer in Bristol, uk and in the past when some of my Canon flashes have broken i have had to resort to using my assistants Nikon flash and the only way I could get it to work was to use a very cheap and crappy wireless trigger which luckily I had on me that day.

Mine is similar to this but older.
http://www.amazon.com/...B002W3IXZW

They will work but only in the manual mode.

iTTL and TTL are proprietary

Kinda… It's not elegant, and you probably want to use something in between either some triggers or a wein safe sync just to isolate the extra electrical contacts, as these can interfere and confuse camera or flash. You will only get a manual flash, but it will work as the trigger command is the centre pin and that's same with all flashes.

Doable, but not elegant, and rather dodgy, it's a last resort type of thing.