Let's break down the expression step by step:

$\frac{5 + 8 \times (3 + 2)}{9} - 1$

1. First, solve inside the parentheses: $3 + 2 = 5$

2. Now the expression becomes: $\frac{5 + 8 \times 5}{9} - 1$

3. Next, multiply: $8 \times 5 = 40$

4. Substitute this back into the expression: $\frac{5 + 40}{9} - 1$

5. Add: $5 + 40 = 45$

6. Now divide: $\frac{45}{9} = 5$

7. Finally, subtract: $5 - 1 = 4$

So, the value of the expression is 4.

Would you like more details on any of the steps? Here are 5 related problems to practice:

1. $(7 + 3) \times 4 - 8 \div 2$
2. $\frac{9 \times (6 + 2)}{3} + 5$
3. $(2 + 4 \times 5) - 12$
4. $\frac{10 + 8 \times (4 + 1)}{6}$
5. $12 \div (3 + 1) \times 5 - 3$

Tip: Always follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).