What router to get? Dual band?

I've just got the interent in my new flat and the service provider (sky) have given me a router but the range seems poor.

I currently use my iPhone and PC through the wireless and my xbox through the wires connection.

My PC is too far away to be wired so I bought a wireless adapter (TP-Link TL-WN951N Advanced Wireless N PCI Adapter).

The card can work up to 5ghz so i would like to get a router that can pump that out. My understanding is that if the router does work at 5ghz that means devices that don't support that won't work with it? (iphone etc)

Would i need to get a router that puts out both 5ghz and the normal (2.4ghz?)?

Yes you are correct you would need a dual band router than broadcasts simultaneously 2.5 and 5Ghz. Only a few high end expensive routers do this. Also you would be going against Sky's T&C of service which prohibits the use of any other router other than those supplied. You would need to access sky community to get the setup details to put into the new router
It may be simpler to get a wireless extender or use powerline networking - these use the household wiring instead of a long Ethernet cable. You plug 1 adapter into the Ethernet port of the router and local mains socket the other adapter into the distant PC/Laptop/game console and a mains socket. If you replace the distant powerline Ethernet adapter with a powerline Wi-Fi adapter you can create a local hotspot a good distance from the router.

http://www.solwise.co.uk/net-powerline-av-index.htm

http://www.netgear.co.uk/home/products/powerline-and-coax/
HTH
David