Okay, so I need to solve this equation: 3x + 2(1 + x) = 17, and then find the value of 6x + 5. Let me think step by step.

First, I should simplify the left side of the equation. Let's expand the terms. The equation is 3x plus 2 times (1 + x). So, distributing the 2 into the parentheses: 2*1 is 2 and 2*x is 2x. So that becomes 3x + 2 + 2x. Now, combine like terms. 3x and 2x are like terms. Adding them together gives 5x. So now the equation is 5x + 2 = 17. 

Next, I need to solve for x. Subtract 2 from both sides to isolate the term with x. 17 - 2 is 15, so 5x = 15. Then, divide both sides by 5 to get x. 15 divided by 5 is 3. So, x = 3.

Now, the question asks for the value of 6x + 5. Substitute x = 3 into this expression. 6*3 is 18, and then add 5. 18 + 5 equals 23. So, the value should be 23.

Wait, let me double-check my steps to make sure I didn't make a mistake. Starting with the original equation: 3x + 2(1 + x). Distribute the 2: 3x + 2 + 2x. Combine like terms: 5x + 2 = 17. Subtract 2: 5x = 15. Divide by 5: x = 3. Then 6x + 5: 6*3=18 +5=23. Yep, that seems right. 

Alternatively, maybe there's another way to approach this without solving for x directly. Let's see. The original equation is 3x + 2(1 + x) = 17. If I simplify that, as before, it's 5x + 2 = 17, so 5x =15, x=3. Then, 6x +5 is 6*3 +5=23. So, same result. 

Alternatively, maybe we can express 6x +5 in terms of the original equation. Let's see. The original equation simplifies to 5x +2 =17. If I need to find 6x +5, perhaps there's a relationship between 5x and 6x. Let's think. If 5x =15, then 6x =15 +x. Then, 6x +5 =15 +x +5 =20 +x. Since x=3, that's 20 +3=23. Same answer. 

So, whether I solve for x first or manipulate the expressions, I get the same result. Therefore, the answer should be 23.
Therefore, the value of $6x + 5$ is $\boxed{23}$.
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