We are tasked with simplifying the expression:

\[
s - r(s - 1) - (s + 3)5 - (-3 + r)
\]

### Step-by-step simplification:

1. **Distribute \( r \) in \( r(s - 1) \):**
   \[
   r(s - 1) = rs - r
   \]
   The expression becomes:
   \[
   s - (rs - r) - (s + 3)5 - (-3 + r)
   \]
   
2. **Distribute the 5 in \( (s + 3)5 \):**
   \[
   (s + 3)5 = 5s + 15
   \]
   The expression is now:
   \[
   s - (rs - r) - (5s + 15) - (-3 + r)
   \]

3. **Simplify the signs for the negative terms:**
   \[
   s - rs + r - 5s - 15 + 3 - r
   \]

4. **Combine like terms:**
   - For \( s \)-terms: \( s - rs - 5s = (1 - r - 5)s = -(r + 4)s \)
   - For constant terms: \( r - r = 0 \), and \( -15 + 3 = -12 \)

Thus, the simplified expression is:
\[
-(r + 4)s - 12
\]

### Final Answer:
\[
-(r + 4)s - 12
\]

Do you want more details or have any questions about this solution?

Here are 5 related questions:
1. How would the expression change if \( r = 2 \)?
2. Can you factor the term \( -(r + 4)s - 12 \) further?
3. What if the expression had additional terms like \( + t(s - 1) \)?
4. How would you graph \( -(r + 4)s - 12 \) in terms of \( s \)?
5. What if \( r \) is a function, say \( r(s) = 2s + 1 \)?

**Tip:** Always distribute and combine like terms carefully to avoid mistakes in simplification!

Learn how to simplify the algebraic expression s - r(s - 1) - (s + 3)5 - (-3 + r) using the distributive property and combining like terms. This step-by-step solution is designed for students in Grades 8-10 studying algebra.

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