Bharat,

The first term is 5. Starting with the second term, what is the first digit of each successive term? What should be the first digit of the fifth term?

Penny

I don't know. (The improper use of the equals sign here doesn't make it any easier.)

I don't see any pattern simpler than continuing 54325, 654325, etc, though it's a bit arbitrary & what the 10th term is to be is unclear. The fourth term is not an integer multiple of the third, breaking one obvious pattern.

Prime factorizations are 5, 5*5, 5*5*13, 5*5*173. I do note that
5 = 1² + 4, 13 = 3² + 4, 173 = 13² + 4 but as 3 never appears anywhere this is probably not useful either.

Good Hunting!
RD