Let's define the variables:
- Let \( m \) be the cost of an adult ticket.
- The cost of a child ticket would then be \( m - 5 \) (since it is $5 less than an adult ticket).
Mrs. Franks purchased 20 child tickets for a total of $180. We can express this situation with the following equation:
\[ 20(m - 5) = 180 \]
Now you can solve for \( m \) to find the prices of the adult and child tickets.