To solve the equation \(\frac{2x + 5}{x + 3} + \frac{3x + 2}{x} = 5\), we need to find a common denominator and simplify the equation. Let's go through the steps:

1. **Identify the common denominator**: The common denominator for the fractions \(\frac{2x + 5}{x + 3}\) and \(\frac{3x + 2}{x}\) is \(x(x + 3)\).

2. **Rewrite each fraction with the common denominator**:
\[
\frac{2x + 5}{x + 3} = \frac{(2x + 5) \cdot x}{(x + 3) \cdot x} = \frac{x(2x + 5)}{x(x + 3)}
\]
\[
\frac{3x + 2}{x} = \frac{(3x + 2) \cdot (x + 3)}{x \cdot (x + 3)} = \frac{(3x + 2)(x + 3)}{x(x + 3)}
\]

3. **Combine the fractions**:
\[
\frac{x(2x + 5) + (3x + 2)(x + 3)}{x(x + 3)} = 5
\]

4. **Simplify the numerator**:
\[
x(2x + 5) + (3x + 2)(x + 3)
\]
Distribute \(x\) in the first term:
\[
x(2x + 5) = 2x^2 + 5x
\]
Expand the second term:
\[
(3x + 2)(x + 3) = 3x^2 + 9x + 2x + 6 = 3x^2 + 11x + 6
\]
Combine the terms:
\[
2x^2 + 5x + 3x^2 + 11x + 6 = 5x^2 + 16x + 6
\]

5. **Rewrite the equation**:
\[
\frac{5x^2 + 16x + 6}{x(x + 3)} = 5
\]

6. **Clear the fraction by multiplying both sides by \(x(x + 3)\)**:
\[
5x^2 + 16x + 6 = 5x(x + 3)
\]
Expand the right side:
\[
5x^2 + 16x + 6 = 5x^2 + 15x
\]

7. **Subtract \(5x^2 + 15x\) from both sides**:
\[
5x^2 + 16x + 6 - 5x^2 - 15x = 0
\]
Simplify:
\[
x + 6 = 0
\]

8. **Solve for \(x\)**:
\[
x = -6
\]

So, the solution to the equation \(\frac{2x + 5}{x + 3} + \frac{3x + 2}{x} = 5\) is \(x = -6\).