Will a 50 foot HDMI cable suffer any signal loss?

I have no experience with an HDMI run that long.

Another option, in case you try it and it doesn't work, is an HDMI extender, like this.
It will convert your HDMI cable into two cat 5e/6 cables and then back to HDMI. AFAIK these extenders can go about 250 meters. (The particular one I linked to was just an example; I am not endorsing that particular brand)

To answer this question, yes.

Any extension will suffer signal lost but some are not as significant and acceptable to what is required. Some equipment have built-in regulator as it regulate (maintain) the signal cracteristic close to spicified level.

A very high quality cables; @ 50 feet lenght will not require a booster. Booster is like multiplier so ANY signal (dirty or clean) is boosted to X amount to the level it is set. Converters are different as it converts the signal to be sent. However, resolution will be lost during conversion as well, especially if not properly implemented.

How much are you willing to give to get the resolution you need? cost is your enemy.

One thing you should try is to make your own HDMI cable using shielded CAT 6 cable. The twisted wires reduce interference plus the shield, so if you can get a HDMI male connectors or get a very short and cheap HDMI cable and cut the end to extend it. If this test does not work, at least you can still use the cable, just lose the head.

If you don't want the hassle then (as suggested before) you might look for something like these: http://www.atlona.com/Atlona-1080p [...] 17468.html
http://www.atlona.com/Atlona-Power [...] 17729.html
http://www.atlona.com/ATLONA-HDMI- [...] 17406.html

I have no affiliation with this company or any links I posted.

I suggest using a shielded CAT 6 cable instead of CAT 5 or CAT 5e and you don’t need to get higher than FT4 unless you really want to.