Put them in something like this, and lay the carpet over it.
Depending on the size cord protector you get, you may need to use a box cutter or utility knife to open one or both of the “side” channels. Be careful and use a new blade - the rubbery stuff is meant to withstand years of being walked on, so it can be a bit challenging to cut. You can probably get the coax and Cat5 in the center pre-split channel without much trouble. There won’t be any trouble interference wise with running the cables together for a few feet. Modern coax has four layers of shielding, and Cat5/Cat6 is built to be inherently immune to interference thanks to the internal twisting of the wires. Good phone cable is also twisted pair.
As noted above, coax will get squashed pretty quickly when walked on. I can say from personal experience that Cat5 cable will be ruined faster than you may expect - after a few months in a very low-traffic area in my living room, the cable jacket was split in several spots, leaving the individual wires to get chafed.