For the OP, you have not given any details as to what you need for the car other than low running costs and 5 doors.

So idly looking through Autotrader, here are a few I'd be looking at in order of ascending size. I've worked on the assumption of a little wiggle room re price, so up to £6.5k.

Citroen C1/Peugeot 108/Toyota Aygo. Pretty small with a small boot, but 5 door versions are available on all three. The 1.0 engine is plenty nippy enough for a car that small and light, they are very reliable and very efficient. A 1.2 engine was offered in the C1 and 108, but for a town/city runabout it isn't necessary. You could get into a 2018 example for the budget.

Suzuki Celerio. These are a bit more spacious and practical with a usefully bigger boot despite still being very small. Very reliable and very efficient, you could get into a car as young as 2019.

Dacia Sandero. Similar size to the MG but a bit more space in both cabin and boot. For your usage, it would be best to avoid the diesel, and because of questionable reliability, also avoid the 0.9 TCE. 2018 cars are available within this budget.

The cars SLO mentions are all good and reliable, but you'd be looking at cars from around 2014/5.

I'd favour the Suzuki Celerio myself as the best combination of running costs, space and age of car.