DVI, will carry all of the HDMI video signal just fine.
At 50', if you were to put something else in, I would use a HD-Base-T transmitter/receiver and use CAT-6 between the two end points. Much easier to run, and if you need to switch it out in another half dozen years with something else, you can just swap the end points with whatever comes next.
Still, I would just use what you have right now.
My biggest worry would be that perhaps you may not be able to carry full 1080p information across an older DVI cable that distance. Maybe. Gotta try it first to find out if you do have an issue, but I wouldn't expect you to have one.