Hello, I’m an incoming senior. I have a strong ACT, will have taken 14 AP classes, 4.0 GPA, and excellent extracurriculars. I’m thinking of applying to Oxford (PPE). The issue is with my AP classes. I have received 2 5’s thus far. Next year, I’m taking 6 AP’s next year and I am pretty sure I’ll get another 5. Can I still apply?
Human Geo: 4
Psychology: 4
Seminar: 4
World History: 4
Statistics: 4
AB Calculus: 3
U.S. History: 5
Language: 5
One of those 5’s better be in Calc BC, or you’re wasting your time.
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The 3 in Calc AB is very likely to lead to a rejection, at least in the absence of an absolutely superlative TSA score. Any offer would be conditional on a 5 in Calc BC in any case.
Oxford would much prefer fewer APs with all 5s rather than more with substandard scores (anything less than a 5). APs are easier than UK A levels so from Oxford’s point of view they should all be easy 5s. One or two slips is forgivable, but “failing” six of them is not.
And you said AP score was not that important. 
How strong is your ACT?
I suggest you google the requirements directly on their site. For PPE, the applicable subjects are Calc BC, History (US or World), Micro/macro Econ, maybe US Government.
My daughter was accepted 3 years ago with ‘5’ on USH, Calc BC, and both Econs, plus 35 on the ACT. Results of ‘3/4’ do not count and may work against you. Check if it is possible to not send them at all.
Having the required AP scores is the first hurdle. Passing the TSA and the interview is what gets you in. Good luck!
Either Four APs at grade 5 (including any subjects required for the course you are applying to)
OR
Three APs at grade 5 (including any subjects required for the course you are applying to) plus
plus a score of 31 or above in the ACT or 1460 or above (out of 1600) in the SAT. We do not require the optional essay for either the ACT or the SAT.
I have never said that in the context of UK unis. I tend to be succinct in my answers, so if a user asks about the importance of APs where it is clear they are asking in context of US colleges, I tend not to write a book listing all the exceptions. I can think of several users who can do that verbosely in my stead. 
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I am taking BC fortunately
like 34 35 ish
My two cents - the 3 in Calc AB and 4 in Stats are going to be very hard to overcome. You have to report all scores on your UCAS. Oxford will see those. AP Stats is not a well regarded course at Oxford for establishing your math credentials. Calc BC is the standard. Having only a predicted score with that kind of track record means that you are going to have to do very well on the TSA to have a shot at getting shortlisted for interview. That’s where I would focus my energy at this point.
One other data point - in the past two years, Oxford has averaged roughly 750 non-UK or EU PPE applicants. Only roughly 60 offers made each year to that group of applicants.
Comp Gov is better than US Gov for PPE (it actually lays decent groundwork for the first year politics module).
…you have or you plan to have?
As @Twoin18 said, you are going to want a very strong TSA to overcome all those 3s and 4s (esp in Calc AB), so get practicing!
All exam results must be reported and I believe that you have to sign the UCAS form stating that you have done so. ( My offspring have all completed their degrees but the signature information was relevant for them.)