Transfer Pricing

Hi john.How are you?Hope doing well. I got few issues regarding Transfer pricing which i have listed below.
Ques. Suppose Company X is based in Uk and it has got a subsidiary Y in France.Y is required to remitt 80% profit to X. Full credit is given by UK tax authorities for tax paid overseas.
Corporation Tax: UK=30%, France =25%
Profit before tax(PBT) of Y= $100,000.(We assumes we deal in dollars)
Witholding tax of 5% needs to be paid by Y for any remittance.
So my thought process dealing the question is below,
PBT of Y =$100000
Tax paid@25% =(25000)
Profit after tax =$75000
Remittance to UK= $ 60000
Witholding tax = $ (3000)
Profit retaied by Y=$15000( Which is 20% of PAT)
FOR X though,
They received = $55000(Net of witholding tax)
Extra tax to be paid =$( 3750)
(75000*.05%)
Net Cash flow from =$ 51250
( Y )
Am i correct on this John? I am confused like Do X will get any tax credit for witholding tax paid by Y on the X remittance so basically Y is paying 25%+5%=30%.So there should not be extra 5% paid by X to uk tax authorities.Or we assume X don’t get tax credit for any witholding tax paid by Y and the the above procedure i mentioned is correct.
Thank you.