I'm assuming that the $5K budget must include the display as well as the audio components. As near as I can tell, the display is going to take up pretty close to half the budget, leaving $2500 or so for audio. A PS3 seems like a no-brainer decision at this budget level for all the features it brings to the table (Blu-Ray, upconverting DVD, wireless streaming music server and web browser, built in hard drive...Oh...and games). So after that you have $2100 left.
You have a large space so a good sub is needed, something like a Hsu VTF-2 MK3 for $499 as in Clint's second link, leaving $1600. I'm certain the STF-1 in the first link would not be enough sub for the size of your space. Even if you budget $1000 for speakers, which is still lower than I'd like to see for a good five speaker set (a stretch to the Axioms in Clint's first link would be a good choice), that leaves only $600 or less for a receiver. The Yamaha in the first link is a solid choice for the money.
Clint has offered some fine recommendations to think about, but boy does that display eat into the budget. It really forces some compromises in other areas, but with a room that big I'd rather not see you skimp on the sub. And for the price of the PS3, your not going to really save enough going with other options, unless you go with the cheap of the cheap DVD players which probably isn't a good idea either.