Yes it is possible to connect them all together, using RJ45 in-line couplers, but it isn't ideal. If you need to use more than one or at the most two couplers to stitch them all together I think you'll be creating a recipe for trouble.
An RJ45 lead can theoretically be up to 100 metres long so you should be able to buy, quite cheaply, a single lead to go the distance you want. Alternatively if you know how to do it you could buy the cable, two plugs and a crimping tool and make one to suit.
If you are running a lead into another room try not to bend it too tightly arounds the corners and beware of things like the spiky carpet grippers if you're trying to tuck it out of the way.
Let us know how you get on.
Why don't you use some powerline adapters. They will use your installed electrical wiring to deliver the network connectivity to your xbox. Plug the main powerline adapter next to your ISP router, and the other one near your xbox power supply point. No fuss.
Picking pebbles on the shore of the networking ocean
So I would just like to put this out there.... make a Ethernet cable the normal way.... it's cheap. Couplers cost about the same as a new wire.
That being said if you really want to make it work and you have zero money, you can always cut the ends off and twist matching colors together... should work in theory but it will bring the cable drastically out of spec.
Let me just restate that is an absolute last option
[/u]. To be used only when you have no choice and no money or no time to go buy more. I've actually done this a few times to see if it is possible and to see how much it kills the connection... just because I wanted to see JUST how much the twists matter. The result is 175ft vs 100m(300ft) and then for each set of twist connections like that you can subtract signal quality and distance. Stranded wire generally does this better then solid core.
Now let me put something out there that will just put TheBishop in the fetal position crying for the standards gestapo. When it comes down to it more often than not your not pushing the 300+ foot limit of cat5 inside your house. In your standard cat5 connection you only have to concern yourself with your transmit and receive pairs.
You transmit on pins 1 and 2 of your cable
You receive on pins 3 and 6 of your cable
That means pins and cables 4,5,7&8 do not do ANYTHING for you on your standard configuration aside from fill the wire and help with noise cancellation. (and keep you in spec)
This means a few different things. First you can take one long wire and cut the head off and make 2 if you have an existing cable already in place as long as you put the cable in the right pin slots. Second you have just doubled the amount of useful cable in your possession at the cost of signal distance and clarity.
Now I'm just going to be an absolute target for those who love standards and say:
You don't even need cat 5 you can mix and match 22-24 AWG copper coated wires as long as you stay under 130ft and connect them to pins 1,2 and 3 and 4. Because at the end of the day... cat 5 is just copper wire (aprox 22-24 awg) with twists and if you take the twists out and use non-standard connections you simply limit the quality per distance because you are removing the EMI interference protection.
Here is an interesting thought 0000000000 awg wire would be REALLY thick wire. If you had 2 of them set for transmit and receive with tons of power running through them over 10 miles the wire could be completely unprotected and not lose signal at all though states of on and off. At the end of the day it's all just copper wire getting a little just running into it.