I never said 5ghz was faster than 2.4

By putting Gaming and Video on 5 ghz, u run less interference with someone on a laptop on Youtube say down loading a video. Or whatever else downloading songs or Utorrenting. That's all

This way you get the highest bandwidth for gaming or Netfliks whatever on 5ghz.
There are routers that do this either 2.4 or 5ghz or for a few $$$ more will do both at the same time.

I did not use 5 ghz for distance as if he is in a normal average home on the same floor it will not be an issue for this regardless of 2.4 or 5ghz.

Secondly, You cannot split a digital signal, unless you want to buy some more electronics.

Not sure where you are but if your one HS with Cable then gonna need to goto their cable modem first anyways. From that go to a router, ( Dlink, Linksys, Cisco ) I don't care.
The only way your gonna run two or three Networks ( LAN ) within is through CAT6 or 5 or 4 or 3 or 5 or 5e I don't care.
You cannot go wireless to wireless with routers. If you need to extend or go wireless from the router to another you need a bridge or extender. Linksys WES610N 4-Port Dual-Band N Entertainment Bridge. See staples $79.99 they are. you can put this near your amp, tv, blu-ray using Catx and go wireless to the router on 5 ghz. with this bridge. There is no need to run Catx cabling.
Also, I don't care what the router is advertised at 1ghz or 500 mbs or 300mbs your internet connection unless you are fibre optics and paying 100's per month I would imagine is only around 80 mbs. so you are not going to reach the 300 mbs the router says it is capable of. And if the remote site puts out 1ghz uploads and you are the only one downloading your not going to get it.

As for Dlink, Linksys, Cisco, Netgear there all good. I have a Dlink 815 and my daughter is on Xbox live playing Black OPs or HAlo, Youtubin music on her iPhone and I am wireless with my tv watching Netflicks upstairs, my dlink router is in the basement and I never yet, had an issue.

Pioneer sc-1525
M80 HG Cherry