I second what others have said, 5K is nowhere near enough for halls and living costs, even the cheapest halls will probably be 3.5-4K, and you sometimes dont have a choice. The pp who made that comment is grossly irresponsible.
My DS just started, his halls in a northern uni are 5.3K. He gets min loan so we will top that up to pay halls fees each term, then give him a weekly allowance, for food etc.
However, he also worked in 6th form and has that money as a buffer. He is also going to look for work again after xmas.
Does or can your DD work at the moment, to save some money up before she goes? Or can she do a gap year and save up?
Also remember your outgoings will drop when she has gone, we are amazed at how much less food we buy for 3 instead of 4! So you may be able to budget to pay her some of what you save.
You maybe need to work out exactly how much she will get and how much halls are in her preferred unis. Remember you can take your pension contributions into account when working out your income.
Can I suggest you get this thread moved to the Higher Education forum, as there are already threads on there about living costs and you may get more detailed advice. Also, when the time comes to apply for halls, ask advice on that forum, as people will know the most cost effective place for her chosen uni.