I've been playing bass for 5-6 years now, and while I have a 5-string bass I've never really taken the fifth string into proper use. The thing is I'm having trouble seeing when I can/should use it.
I've gotten the opportunity to join a semi-technical death metal band, currently just on session-basis, and I want to use the fifth string as they tune relatively low.

The tuning they're using is, I believe, two steps down (C,F,A#,D#,G,C) and I was wondering whether or not I should tune my 5-string bass to C,F,A#,D#,G (the thickest of the strings being the C) and just play it like that. Would that be completely stupid, and am I completely off? Could I get some guidelines or something of the sort?

Certainly a reasonable choice, just choose to add the extra string on either the top or bottom, wherever you think you'll use it more. Having a low G can give you some issues with getting a decent tone on those notes from an amp, and you'll also need some really heavy strings. Adding an extra string on top is nice if you'll use it.

If it was me I would tune as you described. I used to play a 6 string in a screamo band, and i tuned it just like a regular guitar and did counter melodies to whatever the guitar was doing.

Not a bad idea. I don't play a five-string, but have often thought about getting one - if/when I do, I'll be keeping it to standard and tuning the fifth string to a low B - primarily because I'm generally playing in Standard or D tunings, so I'd mainly do it because I'm too lazy to change tuning.

However, if a low C is as low as you will find yourself going, no reason to tune it any other way. The other thing to do would be to tune it to G,C,F,A#,D#. This would give you a slightly lower range to work with.

I've tuned it to C,F,A#,D#,G now, and I guess it sounds alright. The thing is that all the strings are really tight now, but I guess that if I tune them to the lower equivalents they would be lose as fuck?

When tuning two steps down, you are likely to experience the strings becoming looser - higher gauge strings can stop this if it becomes uncomfortable to play/messes up your sound.

It all depends on what you feel more comfortable doing. Personally in my band I keep my bass tuned in B-E-A-D while the guitarists play in a different tuning. I have a few reasons for that. First of all I don't want my bass to be crazy low because I want to keep a bit of brightness and clarity in my sound. The way I see it (in my own case, many will disagree) guitarists tune down because they -need- that low punch and sound. Bass guitars automatically have that those huge, low frequencies going on. The other reason is that this forces me to become much more familiar with my instrument by transposing a lot, and as a result I tend to play bass lines not totally similar to what the guitarists are doing. It helps with the creativity loads. Of course you can definitely be creative with the same tuning, but I'm just putting another idea out there.

And if you like tuning lower, just like TheUglySoldier said.. get some thicker gauge strings. I have basses tuned to A standard and G standard and they aren't floppy in the least. But some people like tuning lower with smaller guages cause it's more comfortable for them to play with their fingers... for instance the bassist in scrotesc who also played in goatwhore briefly after Pat left. his strings weren't too much thicker than some of my guitars! but he was able to play faster with his fingers. So it's also with what your comfortable with as well.