To add the fractions, we need to find a common denominator for all three fractions.

The common denominator for 3ab, 5a²b, and 2ab² is 6a²b².

So, the expression becomes:

(5m/3ab) + (2n/5a²b) - (7p/2ab²)

To get each fraction to have a denominator of 6a²b², we need to multiply the numerators and denominators by whatever is necessary.

So, the expression becomes:

(10m/6a²b²) + (4n/6a²b²) - (21p/6a²b²)

Now that all three fractions have the same denominator, we can add the numerators together:

(10m + 4n - 21p)/6a²b²

Therefore, the final simplified expression would be:

(10m + 4n - 21p)/6a²b²