To find the condition for which the expression (15n^3 + 6n^2 + 5n + x)/n is not an integer, we need to analyze the different terms in the expression and their relationships with each other.

Analysis of the expression:
The given expression is (15n^3 + 6n^2 + 5n + x)/n.

Breaking down the expression:
- The term 15n^3 is a cubic term in n.
- The term 6n^2 is a quadratic term in n.
- The term 5n is a linear term in n.
- The term x is a constant term.

Condition for the expression to be an integer:
For the expression to be an integer, the numerator (15n^3 + 6n^2 + 5n + x) should be divisible by n without any remainder.

Condition for the expression to not be an integer:
For the expression to not be an integer, the numerator (15n^3 + 6n^2 + 5n + x) should not be divisible by n or should have a remainder when divided by n.

Analysis of the terms:
1. The term 15n^3:
- This term is a multiple of n^3, which means it is divisible by n.
- Any multiple of n^3 is divisible by n without any remainder.

2. The term 6n^2:
- This term is a multiple of n^2, which means it is divisible by n.
- Any multiple of n^2 is divisible by n without any remainder.

3. The term 5n:
- This term is a multiple of n, which means it is divisible by n.
- Any multiple of n is divisible by n without any remainder.

4. The term x:
- This term is a constant term and is independent of n.
- The term x may or may not be divisible by n.

Combining the terms:
Since the terms 15n^3, 6n^2, and 5n are all divisible by n without any remainder, the expression (15n^3 + 6n^2 + 5n + x) will also be divisible by n without any remainder.

Condition for the expression to not be an integer:
Therefore, the only condition for the expression (15n^3 + 6n^2 + 5n + x)/n to not be an integer is when the constant term x is not divisible by n. Hence, the correct answer is option C) x is not divisible by n.