B&W Speakers

Given the size of your room, I'd recommend the 805S with a pair of REL Quake or R205 subs (yes, I said "pair" for a 12' x 14' room). While I like my Green Mountain Audio speakers better, I have owned the N805 (along with a REL Strata III) and did enjoy the combination.

Stick with the 800 series within the B&W offerings, and I'd look at the "S" or "D" speakers within the 800 family. I'd also think you'd be better off with the 805S + subs than the 804D.

...and save some money for room treatments.

I'd also recommend looking at other options other than B&W, partly because I'm not a fan but in particular because I've heard them extensively with Linn amps and I did not find the pairing to be synergistic. If you let us know what type of sound you're looking for I'm sure you'll get a bunch of good alternative suggestions, some of which will undoubtedly pair better with your Linn amps. Best of luck in your search.

Agiaccio, If you are really so keen on getting a pair B & W speakers then if you don't mind buying used, just look in the for sale section and see what is the highest up the B & w range you can get for your $5k, they seem popular speakers and are always for sale used.Check the the whole site coz there has been lots of threads regarding B&W's.
It seems to be a bit of a pointless thread/post as your mind is already keen set upon getting you purchasing a pair of B&W speakers.
I have heard the 801/802's with high end Classe gear, and IMHO, I could personally not think (to my ears and wallet) of a worse way of being relieved of a lot of my cash, each to their own, just my penny opinion after a listening. If you are successful in buying a good pair that sound good to your ears, then kudos to you sir, its what its all about, enjoy them!. But if I were you with 5k to spend I would listen to what others have to say, go listen and then dispel, its your money and your ears that in the end count. There are loads of seriously good other makes of speakers for around that non small amount of cash you have to at your disposal.
Good hunting.

I have similar room dimensions albeit a little smaller. I'm currently running a pair Signature 805's with a Velodyne DD-10. This combination offers the most flexibility in terms of room positioning and still offers a nearly full range
sound. I would be very hesitant to go with any larger model
without some serious room treatment.

Good luck

It is just a question of whether you can accommodate the larger footprint of the 804 or 803. The 805 is a fantastic speaker, but lets face it, it is a monitor/bookshelf dweller that is seriously lacking in bass. It is a small speaker, and it just isn't there. It will not sound better than the 804 or 803 in ANY room. The 805 may make more sense ergonomically/physically in that room, but it won't sound better.

The 804 is just a better speaker. The 803S is even better. I think the 803S is the best choice if you can accommodate the footprint. It is worth the upgrade over the 804. The 804 leaves something to be desired in the bass department. The 803 is balanced better.