Coax directly to box vs. through face plate

Based on the symptoms so far -- this isn't a dodgy tuner, or a bad cable. This leaves one possibility: something in the bedroom is spewing RF garbage on VHF channel 5, and moving the TV further away from it causes it to pick up less of the garbage, allowing it to "hear" the TV station on that channel.

Can you try moving the TV from the living room into the bedroom? If the living room TV can't pick up channel 5 while in the bedroom, even with an antenna directly attached, then that would lend serious credence to the RFI theory. From there, it's a matter of unplugging things until channel 5 comes back in...

You might try replacing the splitters. I had one outside a condo failing in such a way that it caused low frequency signals (<50 MHz) to be severely attenuated but higher frequency signals passed quite well. The result was that analog U.S. television channels 2 through 4 were garbage, 5 and 6 were snowy, and the cable modem worked very poorly. In this case, I think the splitters were degraded by flooding (high river levels submerged them for a couple days).