Let's start by defining the variables and the situation described in the problem.
- Let \( m \) be the number of marbles originally in each bag.
- The student has 5 bags of marbles, so the total number of marbles originally is \( 5m \).
- After adding 10 marbles to each bag, each bag contains \( m + 10 \) marbles.
- The total number of marbles in all the bags after adding the 10 marbles to each is \( 5(m + 10) \).
We know that this total equals 80 marbles:
\[ 5(m + 10) = 80 \]
This equation can be solved to determine how many marbles were originally in each bag.