I'm a non-U.S. citizen who was on an F1 Visa that paid FICA Taxes as a Resident years 5-6 in the US.My OPT portion of the visa ended and I permanently returned to the UK. Can I claim back the FICA taxes I paid since I no longer have a visa to live or work in the US?
After five years on an F-1 visa, you become a resident alien. At that point there is no longer an exemption from FICA, unless employment is on-campus. (The on-campus FICA exemption applies to all students, not just those on visas.)
Not living or working in the USA does not entitle you to a refund of FICA taxes.
Specifics from the IRS are here: https://www.irs.gov/individuals/international-taxpayers/foreign-student-liability-for-social-security-and-medicare-taxes