<Question>
Let $f(x) = 2x-3$ and $g(x) = x+1$. What is the value of $g(f(5)-1)$?
</Question>

<think>
<Plan_1>
Okay, let's see. I need to find the value of g(f(5) - 1). Hmm, let me break this down step by step. First, I remember that when dealing with composite functions, I should work from the inside out. So, the innermost function here is f(5). Then, whatever result I get from that, I subtract 1, and finally, plug that into g(x). Let me make sure I get each step right.

Starting with f(5). The function f(x) is given as 2x - 3.

<prompt_1.1> Calculate f(5) using the function f(x) = 2x - 3 as per the above plan. </prompt_1.1>
-----

Alternatively, maybe I can approach it differently. Let's first compute f(5).

<prompt_1.2> Explore an alternative method to solve g(f(5) - 1) as per the above plan. </prompt_1.2>

Alternatively, maybe I can think of it as g( (f(5) -1) ). So first compute f(5), which is 7.

<prompt_1.3> Re-evaluate the steps to ensure accuracy in the solution as per the above plan. </prompt_1.3>

Wait, but let me check if I interpreted the functions correctly. f(x) = 2x -3, so when x is 5, it's 10 -3 =7. Then subtract 1, get 6.

<prompt_1.4> Re-confirm the interpretation of functions and the solution as per the above plan. </prompt_1.4>

Alternatively, maybe there's a different way to combine the functions. Let me see. If I first find f(5) -1, that's 7 -1 =6.

<prompt_1.5> Consider another approach to solve g(f(5) - 1) as per the above plan. </prompt_1.5>

Alternatively, if I had to compute g(f(x) -1) in general, maybe there's a different approach, but since the question is specific to x=5, that's unnecessary here.
But just for practice, let's see: Suppose we first find f(x) -1, which is (2x -3) -1 = 2x -4. Then g of that is (2x -4) +1 = 2x -3. Wait, interesting. So g(f(x) -1) simplifies to 2x -3. Then plugging x=5 gives 2*5 -3 =10 -3=7. Wait, that's the same result as before! So even if we first create a general formula, we still get 7. So that's another way to confirm the answer.
</Plan_1>

<Execution_1>
<execution_1.1>
So replacing x with 5, that would be 2*5 - 3. Let me calculate that: 2*5 is 10, minus 3 is 7. So f(5) equals 7. Got that down.

Next step is subtracting 1 from f(5). So that's 7 - 1, which equals 6. Okay, so now I have f(5) - 1 = 6.
</execution_1.1>

<execution_1.2>
Then subtract 1 from that, so 7 - 1 = 6. Then plug 6 into g(x). Since g(x) is x + 1, that would be 6 + 1 = 7. Wait, that's the same result. So either way, it's 7.
</execution_1.2>

<execution_1.3>
Then subtract 1 from that. So 7 -1 =6. Then plug 6 into g(x). Since g(x) is x +1, that would be 6 +1 =7.
</execution_1.3>

<execution_1.4>
Then plug that into g. So g(6) is 6 +1 =7. That seems straightforward.

Wait, but let me make sure I didn't mix up the order or anything. The problem is g(f(5) -1). So first compute f(5), subtract 1 from the result, then plug that into g. Yes, that's correct. Let me verify each step again.

First, f(5) = 2*5 -3. 2*5 is 10, minus 3 is 7.
</execution_1.4>

<execution_1.5>
Then, plug that into g. So g(6) is 6 +1 =7. So same result.
</execution_1.5>
</Execution_1>

<Plan_2>
Based on execution_1.1:
Now, I need to plug this result into the function g. The function g(x) is given as x + 1. So wherever I see an x in g(x), I replace it with the result from the previous step, which is 6.

<prompt_2.1> Calculate g(f(5) - 1) using the function g(x) = x + 1 as per the above plan. </prompt_2.1>
</Plan_2>

<Execution_2>
<execution_2.1>
Therefore, g(6) would be 6 + 1. Let me compute that: 6 + 1 equals 7. So g(6) is 7. Therefore, putting it all together, g(f(5) - 1) equals 7.
</execution_2.1>
</Execution_2>

<Plan_3>
Based on execution_1.1, execution_2.1:
Wait a second, let me double-check each step to make sure I didn't make any mistakes. It's easy to mix up signs or miscalculate, so verification is key here.

<prompt_3.1> Verify the calculations for f(5), f(5) - 1, and g(6) as per the above plan. </prompt_3.1>
</Plan_3>

<Execution_3>
<execution_3.1>
First, f(5): 2*5 is 10, minus 3 is indeed 7. Then, 7 - 1 is 6. Then, g(6) is 6 + 1, which is 7.
</execution_3.1>
</Execution_3>

<Plan_4>
Based on execution_3.1:
Let me also check if I substituted the functions correctly. f(x) is 2x - 3, so f(5) is definitely 2*5 - 3. No issues there.

<prompt_4.1> Re-verify the substitution and calculations as per the above plan. </prompt_4.1>
</Plan_4>

<Execution_4>
<execution_4.1>
Then, subtracting 1 from 7 gives 6. Then, g(x) is x + 1, so plugging 6 into g gives 6 + 1. All steps seem correct.

Alternatively, maybe I can plug f(5) -1 into g(x) directly. Let's see. Let me write out g(f(x) -1) in general. So f(x) is 2x -3, so f(x) -1 is (2x -3) -1 = 2x -4. Then, g of that is (2x -4) +1 = 2x -3. So g(f(x) -1) simplifies to 2x -3. Then, substituting x=5, we get 2*5 -3 =10 -3 =7.
</execution_4.1>
</Execution_4>

<Final_answer>
Therefore, the value of $g(f(5)-1)$ is $\boxed{7}$.
</Final_answer>
</think>