Can I study PPE at a top university? (With a grade 5 in gcse foundation maths)

I’m currently predicted A*AAA (politics, philosophy, economics, AS core maths ). My gcse’s are not great… Is it still possible I can apply to Russell groups?

In your circumstances you would be best asking each university individually to see whether they will accept your AS in core Maths in place of the normal grade in GSCE
Generally a higher GCSE is required for Economics courses but not Politics courses. It might also be worth looking at straight Politics courses or Politics and International Relations if your Maths proves a problem. Alternatively take a higher paper in Maths in year 13 and show it as pending but your first course of action needs to be to seek the universities advice.

I think the better question is if you struggle with maths why are you aiming for a course including very mathematical elements like economics?
I would suggest you consider politics and philosophy joint honours courses instead if you find maths a challenge (or related things like political economy, international relations, war studies etc).
Core maths will not meet the requirements for coursed needing A-level Maths and I don't think will ameliorate a weak GCSE Maths grade for those courses that don't require A-level Maths which often require an A or equivalent in GCSE Maths.

Many universities do not require A level Maths for PPE and loads dont for Economics. Some high end do but not everywhere. Most have GCSE restrictions and usually want grade 6 Maths but AS is a higher level than GCSE. Anybody sitting foundation can only get grade 5 so it doesnt mean they are bad at Maths and might have achieved higher if they hadnt been placed in a foundation class.

Here is a list of some of the better universities not requiring A level Maths for Economics, Exeter, Loughborough and Manchester dont require A level Maths for PPE.

Economics without A level Maths

Aberystwyth grade 4
Aston grade 5
Bangor grade 4
East Anglia grade 5
Essex grade 5
Hull grade 4
Kent grade 5
Lancaster grade 6
Leicester grade 5
Loughborough grade 6/7
Nottingham grade 7
Queens Belfast grade A
Reading grade 6
Royal Holloway grade 7
Stirling grade 4
Srathclyde grade 6
Surrey grade 7
Sussex grade 6
Swansea grade 5

I didn't say that they all require A-level Maths, I said for those that do Core Maths won't suffice. And I noted that many that don't require A-level Maths require a high grade in GCSE Maths.
If they were on foundation then it indicates to a point they were not overly strong in maths at the time at least, and if they were not able to manage the higher GCSE topics I think that would be a real struggle at degree level when they need to cover the whole of A-level Maths in a few months and necessarily will be assumed to have complete mastery over the GCSE topics. Degree level economics is ultimately a relatively mathematical affair - certainly at A-level and beyond standards.
Also given the OPs predicted grades I suspect they would be intending to target universities with fairly high entry criteria if able to, and so may find not only a degree in e.g. politics and philosophy more suited to their strengths, they would have more options among that calibre of unis e.g. LSE etc.
Finally such courses often provide ample opportunity to sample economics-related topics e.g. political economy, history of economic thought, philosophy of economics/social sciences, public policy related topics which invariably are underpinned by economic concepts. They simply then don't need to be doing the actual maths involved in economic theory. Thus playing into both their interests and strengths. It's better for them to choose a course that plays to their strengths and interests and not just pursue an interest for which they are un- or underprepared for and/or unsuited to.