The given expression is:

\[
-5(x - y) + 2y
\]

### Step-by-step simplification:

1. Distribute \(-5\) across \((x - y)\):
   \[
   -5(x - y) = -5x + 5y
   \]

2. Now substitute this back into the original expression:
   \[
   -5x + 5y + 2y
   \]

3. Combine like terms (\(5y + 2y\)):
   \[
   -5x + 7y
   \]

### Final simplified expression:

\[
-5x + 7y
\]

Would you like further details or have any questions?

Here are five related questions for further practice:

1. Simplify: \(-3(x - 2y) + 4y\)
2. Simplify: \(-2(2x - y) + 3x\)
3. Simplify: \(-7(x + y) - 5y\)
4. Expand and simplify: \(-4(2x - y) + 6y\)
5. Combine like terms: \(8x - 3y - 2x + 7y\)

**Tip:** Always distribute negative signs carefully to avoid sign errors.

Simplify the algebraic expression -5(x - y) + 2y with a detailed step-by-step solution. Learn how to apply the distributive property and combine like terms in this problem, suitable for students in Grades 6-8.

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