To combine like terms and simplify the given expression, let's follow these steps:

Given Expression:

$2\left(\dfrac{1}{5}m-\dfrac{2}{5}\right)+\dfrac{3}{5}$

Step 1: Distribute the 2 across the terms inside the parentheses:

$2 \times \dfrac{1}{5}m - 2 \times \dfrac{2}{5} = \dfrac{2}{5}m - \dfrac{4}{5}$

So, the expression becomes:

$\dfrac{2}{5}m - \dfrac{4}{5} + \dfrac{3}{5}$

Step 2: Combine like terms:

Combine the constants $-\dfrac{4}{5}$ and $\dfrac{3}{5}$:

$\dfrac{2}{5}m - \left(\dfrac{4}{5} - \dfrac{3}{5}\right) = \dfrac{2}{5}m - \dfrac{1}{5}$

Final Simplified Expression:

$\dfrac{2}{5}m - \dfrac{1}{5}$

This is the simplified expression after combining like terms.

Would you like further details or have any questions? Here are five related questions for practice:

1. Simplify: $\dfrac{3}{4}x + \dfrac{1}{2}x$.
2. Combine like terms: $3y - 4 + 5y + 2$.
3. Simplify: $4\left(\dfrac{2}{3}n - \dfrac{1}{6}\right) + \dfrac{5}{6}$.
4. Combine and simplify: $\dfrac{7}{8}p - \dfrac{1}{4}p + \dfrac{3}{8}p$.
5. Simplify: $\dfrac{2}{7}a + \dfrac{3}{7}a - \dfrac{5}{7}$.

Tip: When combining like terms, always pay attention to the signs (positive or negative) in front of each term!