We know Moses was raised in Pharaoh's kingdom. From Exodus 7:7 we know Moshe was around 80 when he lead the Jewish people out of Egypt. But how old was Pharaoh during all of this?
Rashi to Shemos 1:8 cites a dispute as to whether the Paroh who initiated the decree of slavery was the same Paroh as previously or not. He further writes on 2:23 that when it says Paroh died then it doesn't mean literally.
If we assume according to the opinion that Paroh died in 1:8, then the new king reigned for at least 113 years (as per the calculations I cite here) until Bnei Yisrael left Mitzraim.
If we assume according to the opinion that Paroh did not die in 1:8, then: the Bnei Yisrael were in Mitzraim for 210 (as per the tradition I cite here), preceded by nine years that Yosef was on the throne, preceded by Yosef's first meeting with Paroh. As such, he would have been on the throne for at least 219 years.
I say this is a partial answer, because while this does not tell us exactly how old Paroh was, it gives us a lower bound. Obviously these numbers are only according to Rashi’s understanding of the Pesukim.