Five weeks is far, far too young for her to have been taken away from her mother. It was totally irresponsible for the 'breeder' (and I use that term in the loosest way possible) to have sold the kittens so young, and smacks of caring more about the cash than the health and wellbeing of the kittens. I highly doubt she is even fully weaned unless she was an extremely early starter. To be well-adjusted a kitten shouldn't leave it's mother until it is at least 8 weeks old (six weeks seems to be the norm, but that doesn't mean it's correct). So not using the litter tray will probably turn out to be the least of your worries, unfortunately. I'm guessing at 5 weeks she probably won't have been wormed either, so it's important to take her to the vet as soon as possible.
With regards to the litter tray - move it to her favourite toileting spot, and pick up a poo off the floor to put in it. After her meals, put her in the tray and she should get the hang of it quite quickly (the smell of poo will remind her what to do). Once she's got the hang of it, you can move the tray back to your preferred spot - but make sure she knows where it is and don't put it anywhere near her food or water bowls because she won't use it. If she still doesn't use it, you will need to try a different type of litter. Some cats prefer a sand-like texture to the gravel kind. Catsan Clumping Litter is the best I've found, and is very economical because you only scoop out the dirty bits (the wee clumps together to form a ball that you can scoop out easily, leaving only clean litter behind).
For her bed, put a cushion or blanket in her cat carrier and let her use that. It makes things much easier when you need to take her anywhere, as she will see the carrier as her safe place instead of something to be scared of. Try to discourage her from sleeping under the sofa, because if someone tries to use the recliner without realising she's underneath she could get badly injured.
With regards to food, all the supermarket brands like Go Cat and Whiskas are crap - very little meat content (average is about 4%) and full of sugar and additives. She needs to be on a high quality kitten food like Arden Grange, which is very cheap if you buy a breeder bag online from Berriewoods (it costs me £8 a month to feed my two adult cats). Alternatively something like James Wellbeloved or any of the other 'premium' brands that you can get in Pets at Home. When choosing a food you should look for the highest meat content and the smallest ingredients list, and avoid anything that has a list of chemicals clogging up the ingredients list. You will need to change the food very gradually to avoid upsetting her system, and measure it out to ensure she is getting the right amount (which is probably less than you'd think). If you want to give her wet food, the best one is Nature's Menu which is 70% meat. Again, all the usual candidates like Whiskas and Felix are poor quality with very little meat content.