Doubt from one of the quora examples

Questions & Problems
1

Question:

If the integers m and n are chosen at random between 1 and 100, then find the probability that

7^m+7^n

is divisible by 5.

I approached this way-

The last digits of the powers of 7 follow the pattern

7,9,3,1,7,9,3,1,...

For 7^m+7^n to be divisible by 5, its units digit should be 0 or 5

this happens when the last digits are 7+3=10 or 9+1=10. So the two powers must have the same parity, but they must be different powers. For even powers,

7^2,7^4,7^6,...,7^{100}

there are 50 even powers. Their last digits follow the pattern : 9,1,9,1,…

Similarly, for odd powers,

7^1,7^3,7^5,\ldots,7^{99}

there are 50 odd powers and their last digits follow the 7,3,7,3,.. pattern

I am getting stuck after this. I can’t figure out how to correctly count the number of (m,n) pairs that actually satisfy this condition. How to count the number of valid pairs (m,n) and is my approach even valid?