There is no way anyone could buy, insure and tax a car for that.
No but then you're not really comparing like for like.
If your current (no car or allowance) take home pay is X and you take a company car, your take home pay will be X minus whatever company car tax you pay - eg you will take home less than you do at present.
If your salary is X and you take the £5k allowance, your take home pay is X plus whatever the 5k works out to per month take home (at 20% tax, 11% NI, that's approx £250-£300 extra per month. eg you take home more money each month (from which you have to pay for the car, insurance, repairs, petrol, everything).
So the difference isn't say £55, it's £55 plus £275ish = £330ish or whatever the numbers are.
For £330 a month, you may well be better off with your own car, depending on mileage, whether petrol is included, what sort of car you buy and so on.
Because I don't do big miles, I know that I'm much better off taking the allowance though I do have to do all the admin, etc myself of course.