Simplify the expression. \[ 2 m+\frac{4}{25}+5 n+\frac{6}{25}+8 m-2 n \]

Let's simplify the expression step by step. Start by combining like terms in the expression: \[ 2m + 8m + 5n - 2n + \frac{4}{25} + \frac{6}{25} \] Combine the \(m\) terms: \[ 2m + 8m = 10m \] Combine the \(n\) terms: \[ 5n - 2n = 3n \] Combine the constants: \[ \frac{4}{25} + \frac{6}{25} = \frac{10}{25} = \frac{2}{5} \] So the expression simplifies to: \[ 10m + 3n + \frac{2}{5} \] Thus, the final simplified expression is: \[ \boxed{10m + 3n + \frac{2}{5}} \]