For permanent installation, high voltage and low voltage need (I believe) at least 3" of separation. But, there is little to no chance of electrical interference on typical HDMI runs.
Now, if this is all behind drywall, then you have some other serious considerations if you are thinking that one HDMI cable behind the wall is all that you need.
Multiple HDMI cables and cat5e cables are recommended unless you can easily replace cabling or run conduit.