<Question>
Solve
\[\frac{1}{x - 5} > 0.\]Enter your answer using interval notation.
</Question>

<think>
<Plan_1>
Okay, so I need to solve the inequality 1/(x - 5) > 0. Hmm, let me think about how to approach this. I remember that when dealing with inequalities involving fractions, the sign of the numerator and denominator plays a crucial role. Since the inequality is greater than zero, both the numerator and denominator need to have the same sign. But wait, the numerator here is 1, which is always positive. So, for the fraction to be positive, the denominator must also be positive. That makes sense because a positive divided by a positive is positive, and a positive divided by a negative is negative. So, the denominator (x - 5) has to be greater than zero.
Let me write that down: x - 5 > 0. Solving for x, I add 5 to both sides, so x > 5. 

But hold on, I should check if there are any other considerations. For example, the denominator can't be zero because division by zero is undefined. So, x - 5 ≠ 0, which means x ≠ 5. Therefore, the solution can't include x = 5.

Wait, but when x approaches 5 from the right side, the denominator becomes a very small positive number, so the expression 1/(x - 5) approaches positive infinity, which is indeed greater than zero. On the other hand, if x approaches 5 from the left side, the denominator is a negative number with a very small absolute value, making the expression approach negative infinity, which doesn't satisfy the inequality. So, x has to be greater than 5.

Let me test a value greater than 5, say x = 6.
Plugging into the inequality: 1/(6 - 5) = 1/1 = 1, which is greater than 0. That works. Now, let's test a value less than 5, like x = 4.

<prompt_1.1> Test a value less than 5, like x = 4, to verify the inequality. </prompt_1.1>

What about x = 5?
It's undefined, so we can't include that.

Is there anything else I need to consider? Maybe the behavior as x approaches infinity?

<prompt_1.2> Consider the behavior of the expression as x approaches infinity and determine the solution set. </prompt_1.2>

So, putting it all together, the solution is all real numbers x where x is greater than 5.
In interval notation, that's (5, ∞).
-----

Wait, but let me double-check. The inequality is 1/(x - 5) > 0. Since 1 is positive, the denominator must be positive.
So x - 5 > 0 => x > 5. Yep, that's correct.
</Plan_1>

<Execution_1>
<execution_1.1>
Then 1/(4 - 5) = 1/(-1) = -1, which is not greater than 0. So, that interval doesn't work.
</execution_1.1>

<execution_1.2>
As x becomes very large, the denominator x - 5 becomes large as well, so 1 divided by a large positive number approaches 0 from the positive side. So, it's still greater than 0, but that's already included in x > 5. So, there's no upper bound here except infinity. 

Therefore, I don't think there's any other point where the expression could be positive. The only time 1/(x - 5) is positive is when x - 5 is positive, which is x > 5.
</execution_1.2>
</Execution_1>

<Plan_2>
Based on execution_1.1, execution_1.2:
I think that's all.
The solution is x in (5, ∞).
</Plan_2>

<Execution_2>
No prompt to execute.
</Execution_2>

<Final_answer>
\[\boxed{(5, \infty)}.
\]
</Final_answer>
</think>