Is the group C_5 x C_5 a cyclic group

is the group C_5 x C_5 a cyclic group.
give reasons for your answer
C_5 is cyclic group

No it's not. We know that, for any x in C_5, that x^5 = e. Therefore, for any (x, y) in C_5, we have:

(x, y)^5 = (x^5, y^5) = (e, e)

Hence, no element can generate more than 5 elements, and thus no element can generate all 25 elements.