[tex]\tt Step-by-step~explanation:[/tex]
When the number gets powered, it equals to a number higher than 620 and less than 630. I can safely assume that that number would equal to 625, if the number is 5.
[tex]\tt 5^1=5\\5^2=25\\5^3=125\\5^4=625[/tex]
[tex]\large\boxed{\tt Our~final~answer:~5^4 ~(=625)}[/tex]
