Okay, so I need to solve the inequality 1/(x - 5) > 0 and express the solution in interval notation. Let me start by recalling how to handle inequalities with rational expressions. 

First, I remember that when dealing with inequalities involving fractions, the sign of the expression depends on the signs of the numerator and denominator. In this case, the numerator is 1, which is a positive constant. So the sign of the entire expression 1/(x - 5) will depend entirely on the denominator, (x - 5). 

Since 1 is positive, the fraction 1/(x - 5) will be positive when the denominator (x - 5) is also positive. If the denominator is negative, the fraction would be negative. Therefore, the inequality 1/(x - 5) > 0 simplifies to finding where (x - 5) is positive. 

So, solving (x - 5) > 0 gives x > 5. That seems straightforward. But wait, I should check if there are any restrictions or special cases. For example, the denominator cannot be zero because division by zero is undefined. So x - 5 ≠ 0 implies x ≠ 5. 

Therefore, the solution must be all real numbers x where x > 5, excluding x = 5. But since x = 5 makes the denominator zero, the inequality is not defined there, so we don't include it. 

Let me test a value to the right of 5, say x = 6. Plugging into the original inequality: 1/(6 - 5) = 1/1 = 1, which is greater than 0. So that works. What about a value less than 5, say x = 4? Then 1/(4 - 5) = 1/(-1) = -1, which is less than 0. So that's not part of the solution. 

Therefore, the solution set is all real numbers greater than 5. In interval notation, this is written as (5, ∞). 

Wait, but let me make sure I didn't miss anything. The original inequality is 1/(x - 5) > 0. The critical point is at x = 5, where the expression is undefined. So we split the real line into two intervals: (-∞, 5) and (5, ∞). Testing each interval, as I did before, confirms that only (5, ∞) satisfies the inequality. 

Is there another way to approach this? Maybe by multiplying both sides by (x - 5), but I have to be careful because if (x - 5) is positive, the inequality direction stays the same, but if (x - 5) is negative, the inequality direction flips. However, since we don't know the sign of (x - 5) yet, this might complicate things. 

Alternatively, let's consider that 1/(x - 5) > 0 is equivalent to (x - 5) > 0 because the product of two positive numbers is positive, and here since 1 is positive, the denominator must also be positive. Therefore, x - 5 > 0 leads to x > 5. 

So both methods lead to the same conclusion. Therefore, the solution is x > 5, which in interval notation is (5, ∞). 

Just to recap: The key steps are recognizing that the inequality is determined by the denominator's sign, ensuring that the denominator isn't zero, testing intervals around the critical point, and confirming the solution through substitution. 

I think that's thorough. No steps seem missed. The answer should be (5, ∞).
Therefore, the solution to the inequality is $\boxed{(5, \infty)}$.
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