Prove its not a regular language
Here's a hint: we know that $L = \{x^m y^m \mid m ≥ 1 \}$ is a non-regular language.

Is there some part of $I = \{ a^{5n} b^{3m} c^n d^m \mid m,n ≥ 0\}$ which looks similar to $x^m y^m$?

Could you somehow extract that part?

If you could, could you use the fact that $L$ is not regular to conclude that the extracted part is not regular?

Given this, can you then conclude that $I$ is not regular?