Hi elagazine and welcome to the forum! Sorry to hear that you and your friend are not making the weight loss progress that you hoped for. Let's see what might be going on.
First, though, your friend already has a normal BMI of 23.5 so she doesn't really need to lose weight on health grounds. You are just outside the 'normal' bounds but it won't take too much to bring you back inside.
It sounds like you are losing visceral fat i.e. from round your tummy, even if the weight overall is not coming off, and that is actually the most important thing for your health. We have a great tracker here into which you can put your weight and your waist measurements on a regular basis and watch one or (usually) both go down - do try it.
Anyway, back to the weight issues, these are my thoughts, others may have different suggestions.
In case you wondered, the 5:2 diet helps you lose weight by restricting your overall calorie intake, it's just that most of us find it easier to do this by substantial restriction on just 2 days and eating normally the other 5. (I'm simplifying a bit here, and there are other health benefits too, we hope.)
So my first question has to be what you are eating on the other 5 days. Because although you might have heard that you can eat as much as you like on those days and still lose weight, it ain't necessarily so. You shouldn't need to calorie count on those days, you just eat 'normally', but that means eat your TDEE i.e. the same amount of calories as you are expending. This is affected by your level of activity as well as your own natural metabolic rate.
So if you want to work your TDEE and start counting, that's one way to do it. But the truth is that if you are not losing weight, and you are confident you are sticking to the 500 on fast days, then 'over-eating' on the 'feed days' is almost the only possibility left. So the solution is to cut down on the 5 feed days somewhat. Doesn't have to be every day, in fact some variety in calorie intake might help, but overall.
I say almost the only explanation, because your friend is taking quite a lot of exercise and this can affect weight loss. Of course it burns a lot of calories but I guess she is probably eating more calories too. It also causes inflammation of the muscles which is part of the process by which they develop, and this can means water retention. So in her case her half-marathon planning might be part of the cause too. That's not a reason to stop running of course!
Hope that gives you some food for thought