Solving a word problem involving age differences and algebraic equations.

Problem Statement:

A man is 21 years older than his son. Five years ago, he was 4 times as old as his son. What are their ages now?

Solution:

#### Step 1: Define Variables
Let:
- \( x \) = the current age of the son.
- \( x + 21 \) = the current age of the man (since he is 21 years older than his son).

#### Step 2: Express Ages 5 Years Ago
- The son's age 5 years ago: \( x - 5 \).
- The man's age 5 years ago: \( (x + 21) - 5 = x + 16 \).

#### Step 3: Use the Given Condition
Five years ago, the man was 4 times as old as his son. This gives us the equation:
\[
x + 16 = 4(x - 5)
\]

#### Step 4: Solve the Equation
Expand and simplify the equation:
\[
x + 16 = 4(x - 5)
\]
\[
x + 16 = 4x - 20
\]

Rearrange the terms to isolate \( x \):
\[
16 + 20 = 4x - x
\]
\[
36 = 3x
\]

Solve for \( x \):
\[
x = \frac{36}{3} = 12
\]

#### Step 5: Determine Current Ages
- The son's current age is \( x = 12 \).
- The man's current age is \( x + 21 = 12 + 21 = 33 \).

#### Step 6: Verify the Solution
- Five years ago, the son's age was \( 12 - 5 = 7 \).
- Five years ago, the man's age was \( 33 - 5 = 28 \).
- Check the condition: Was the man 4 times as old as his son 5 years ago?
\[
28 = 4 \times 7
\]
This is true.

Final Answer:

\[
\boxed{12 \text{ and } 33}
\]