Hello,
As far as Projectors go, I really think Sony's SXRD create the most lifelike images. Sony's Digital Projector Technology is so good that almost every Movie Theater that is switching to Digital Projectors (a huge amount due to the myriad savings including no more Shipping of Film Prints)
This Sony SXRD Projector Retails for $4000, but Amazon is selling it for almost $1000 less:
http://www.amazon.com/Sony-VPLHW30AES-300-Inch-1080p-Projector/dp/B005GUAIJW
Here is a Review:
http://www.projectorcentral.com/sony_vpl-hw30es_3d_projector_review.htm
And Here is one from a major A/V Magazine:
http://www.soundandvisionmag.com/article/test-report-sony-vpl-hw30es-3d-hd-projector
With roughly $2000 remaining, I would get the Onkyo TX-NR709 which can be found for around $400. If you live near a Fry's Electronics, they are blowing out 709's and the even better 809 for even less to where the 809 costs around a 709 costs. The major upgrade with the 809 is the addition of the HQV VIda Processor which is one of the finest offered on an AVR/SSP.
For Speakers, I would look at the Klipsch Icon W-14 which retails for $599, but are available from Newegg for $199 a Pair:
http://www.newegg.com/Product/Product.aspx?Item=N82E16882780083
They are available in a Natural Wood Finish or Black Ash. I would get 3 Pairs.
For a Subwoofer, I would go with Dual HSU VTF-2 MKV's. Truly a fantastic Subwoofer and would truly transform your Home Theater into a Theater.
http://www.hsuresearch.com/products/vtf-2mk4.html
They sell for $519 each plus Shipping.
For Cables, Monopriice will save you a fortune and that is the way I would go to stay close to your budget.
While this proposed HT goes slightly over $5000 and does not yet include a Screen, it offers Speakers that are of a way higher quality than what should be possible for $199 a Pair, an AVR that Retails for between $899 and $1099, a Subwoofer than shames many $1000 Subwoofers, and a Projector that outperforms Projectors costing $10,000 just a few years ago. Provided $5000 is not a strict budget, this HT would be outstanding, If the budget is absolute max, I suppose you could go with only 1 Subwoofer, but going with 2 would add so much when working with this big of a Room.
Cheers,
JJ