Okay, let's see. I need to find the value of g(f(5) - 1). Hmm, so first, I should probably figure out what f(5) is. The function f(x) is given as 2x - 3. So if I plug in x = 5 into f(x), that should be 2 times 5 minus 3. Let me calculate that. 2 times 5 is 10, and 10 minus 3 is 7. So f(5) equals 7. Got that part down.

Now, the expression inside the function g is f(5) minus 1. Since f(5) is 7, subtracting 1 gives 6. So now I need to find g(6). The function g(x) is x + 1. So substituting x = 6 into g(x) would be 6 + 1, which is 7. Wait, so g(f(5) - 1) equals 7? Let me double-check to make sure I didn't make any mistakes.

First step: f(5) = 2*5 - 3 = 10 - 3 = 7. Correct. Then f(5) - 1 = 7 - 1 = 6. Then g(6) = 6 + 1 = 7. Yeah, that seems right. Let me verify again. Maybe I can approach it differently. Let's compute the composition step by step.

Alternatively, maybe I can find the composition of f and g first, but in this case, since the problem is g(f(5) - 1), which is not a straightforward composition. It's g applied to (f(5) - 1), not g(f(5)). So first, compute f(5), subtract 1, then apply g. So the steps are correct. 

Another way to check: Let's compute f(5) again. 2*5 is 10, minus 3 is 7. Then subtract 1 gives 6. Then add 1 to 6 gives 7. Yep, same result. I think that's solid. Maybe I can also compute f(5) - 1 in another way. Let's see, f(5) is 7, so 7 - 1 is 6. Then g(6) is 6 + 1 = 7. All right, seems consistent. 

I don't see any errors here. The functions are straightforward linear functions, so the arithmetic should be simple. Let me just recap:

1. Compute f(5): 2*5 - 3 = 7.
2. Subtract 1 from f(5): 7 - 1 = 6.
3. Apply g to the result: g(6) = 6 + 1 = 7.

Yes, that all checks out. I think the answer is 7. Let me check once more. Maybe if I substitute into the functions symbolically. Suppose x = 5. Then f(x) = 2x - 3. So f(5) = 10 - 3 = 7. Then f(5) - 1 = 6. Then g(6) = 6 + 1 = 7. Yep, same answer. 

Alternatively, if I tried to find g(f(x) - 1) as a general function, maybe that's overcomplicating, but let's see. If I wanted to express g(f(x) - 1) as a composite function, it would be g(f(x) - 1) = (f(x) - 1) + 1 = f(x). Wait, that's interesting. Because g(y) = y + 1, so if you input y = f(x) - 1 into g, then g(y) = (f(x) - 1) + 1 = f(x). So in that case, g(f(x) - 1) = f(x). Therefore, for any x, g(f(x) - 1) equals f(x). So in this case, x is 5, so g(f(5) - 1) = f(5) = 7. Oh! That's a smarter way to see it. That shortcut could have saved some steps. But since the problem is specific to x=5, either way works. 

But this also shows that maybe the problem is designed to test if you recognize that g(f(x)-1) simplifies to f(x). That's a nice property. So in general, if g(y) = y + 1 and f(x) = 2x - 3, then g(f(x) - 1) = (2x - 3 - 1) + 1 = 2x - 4 + 1 = 2x - 3 = f(x). So yeah, that's why. So in this case, since the composition simplifies to f(x), then g(f(5)-1) is just f(5) which is 7. That's a clever observation. But even if I didn't see that, the step-by-step approach works too. 

So regardless of the method, the answer is 7. I think that's solid. I don't see any mistakes in the calculations. The key steps are substituting into f and g correctly and performing the arithmetic accurately. All steps check out. Therefore, the final answer is 7.
Therefore, the value of $g(f(5)-1)$ is $\boxed{7}$.
</think>