How to connect audio + video to a Sony STR-DA5300ES receiver?

I just purchased a Sony STR-DA5300ES receiver, which has every input imaginable on its back side. Surfing the net, I saw many suggestions for how to connect a Mac mini for HD and surround sound, but most of the answers were basically "connect the video to your TV's HDMI input from DVI, and connect the audio to your receiver".

Since my receiver is about 15 feet from the TV, connected currently via HDMI, and the receiver seems quite capable, I was hoping there'd be a more elegant solution, where I could get audio + video to the receiver some way, and that the receiver would play the audio but pass on the video to the HDMI connection.

Has anybody done this?

(I guess it'd be better to ask this on a Sony STR-DA5300ES forum, but I'm not sure where those are -- and I'm hoping there are knowledgable others in my boat here.)

Thanks in advance!