If your antenna and the transmitters are separated by a mountain, then the fact the transmitters are only five miles away is small comfort. The fifty miles between you and the Seattle transmitters is not a particularly long distance unless there are obstructions along the way.
My suggestion to you is to type in your address into the TV Fool
TV Callsign Lookup dialog and to study the coverage map for each station that interests you. You might be surprised by what you see.