There are no standardized high-school exams in the USA. The closest things would be SAT/ACT which are taken by college-bound high school students, but they are separate from high school and have zero bearing on graduating from high school.
I don't know of any reason an older person could not take the SAT but also most older students interested in going to university would be admitted under different critera than a 17 year old, and high school grades and SAT might not be relevant at all for someone in his 30s or older.
I don't know of any reason an older person could not take the SAT but also most older students interested in going to university would be admitted under different critera than a 17 year old, and high school grades and SAT might not be relevant at all for someone in his 30s or older.