I don't see how you would control your rappel using 5mm cord, without a special belay device. Not sure if you can get a munter in a D-carabiner using 5mm cord, but i'm not sure you would even want to. A munter uses rope to rope friction to control the decent. Not sure how 5mm cord would hold that kind of abuse.
A standard ATC or a Figure of eight does not give nearly enough friction to hold you with 5mm. A grigri is just useless with that cord diameter.
Having less safety margin might be acceptable in an emergency, but i think this setup will just cause you to hit the deck hard. Before even trying such thing, please also look for the emergency exit or wait for the FD if you are not in direct danger.
Tjin:
You can take 5mm rope and double warp and triple wrap the figure 8 device and that will give you the friction, also if you are truly desprerate for friction you can twist the rope before captureing the "neck" of the figure 8.
Also as memory serves me, I have herd of a supper small figure 8 device that was given to military parchuters that was designed to get them down from places that they may get caught up in. From my understanding, if a parachuter gets hung up in a tree, they can use this figure 8 device, and use either the cord they have in the chute, or that they keep on them. to rappel down to the ground. I need to be clear, I have only heard this, I have never seen this.
Also there is nothing that says you can't flip the figure 8 around and use the smaller side to control the rope, and the bigger side to clip into your harness.
They also now make mini non locking carabiners. I have about 6 of them and they are fun to use and very practical. before you scoff, they are as stong if not stronger than the full sized ones, the only difrence is that they are not good at handeling mutiple lines, or a lot of rope.