Given that $\cot x = -\frac{5}{12}$ and $x$ lies in the second quadrant, we need to find the values of the other five trigonometric functions: $\sin x$, $\cos x$, $\tan x$, $\sec x$, and $\csc x$.

Step 1: Use the cotangent identity

$\cot x = \frac{\cos x}{\sin x}$

Given $\cot x = -\frac{5}{12}$, we can write:

$\frac{\cos x}{\sin x} = -\frac{5}{12}$

Step 2: Express $\cos x$ and $\sin x$ using a right triangle

We can let $\cos x = -5k$ and $\sin x = 12k$ for some positive