As others have said, this should be easily achievable, although the OP hasn't said whether or not she eats eggs, but it would be enormously helpful if she does as they're an excellent basis for cheap healthy meals that are quick and easy to cook.
Bananas and carrots are probably the cheapest fruit and veg and good for snacks or adding to porridge (also very cheap)
Add a basic lettuce and cucumber and you have salad that will last a few days as an accompaniment to baked potatoes, omelettes, pasta etc. I also add grated carrot and thinly sliced red onions soaked in white wine vinegar and have that as the salad that goes with falafels and pittas, or any sort of meat/meat alternatives like burgers or fritters that have been suggested.
You might be able to stretch to some basic spices if you don't already have them, either own brand jars or the Asian branded packs are all under a pound, so cumin, coriander, chilli and curry powder, paprika and garam masala will cost under a fiver so might be manageable and allow you to make a huge variety of different dishes very cheaply, eg dhal, chilli.
Also big packs of frozen garlic and ginger from larger branches of Asda or Tesco usually for about a pound each last absolutely ages and work out very cheap.
But yes, it's also a good question about what you normally eat if you see this as a problem you need help with, say you don't eat much, and don't eat meat or fish, plus do have some food in the house already (not sure how you're counting the 5 days food, 13 days until pay day and when that is - is it 13 days after the 5 days, or 13 days till pay day and you only need to buy food for 8 days, because you already have 5 days covered?)
I would be careful with Gousto, it's ludicrously expensive unless you get an offer, especially for vegan/ovo vegan food because, as this thread has demonstrated, the ingredients cost very little. Plus you have to cancel or else they'll send you a box at full price.