Step 1: Simplify the Trigonometric Identities

Recall the following identities:

1. \(1 + \cot^2 \theta = \csc^2 \theta\)

2. \(1 + \tan^2 \theta = \sec^2 \theta\)

3. \(\csc \theta = \frac{1}{\sin \theta}\)

4. \(\sec \theta = \frac{1}{\cos \theta}\)

Substitute these into the expression:

\[\frac{5}{\csc^2 \theta} + \frac{3}{\sec^2 \theta} + 2 \cos^2 \theta\]

Step 2: Rewrite in Terms of Sine and Cosine

Since \(\csc \theta = \frac{1}{\sin \theta}\) and \(\sec \theta = \frac{1}{\cos \theta}\):

\[\frac{5}{\csc^2 \theta} = 5 \sin^2 \theta\]

\[\frac{3}{\sec^2 \theta} = 3 \cos^2 \theta\]

So the expression becomes:

\[5 \sin^2 \theta + 3 \cos^2 \theta + 2 \cos^2 \theta\]

Step 3: Combine Like Terms

Combine the \(\cos^2 \theta\) terms:

\[5 \sin^2 \theta + (3 \cos^2 \theta + 2 \cos^2 \theta) = 5 \sin^2 \theta + 5 \cos^2 \theta\]

Factor out the 5:

\[5 (\sin^2 \theta + \cos^2 \theta)\]

Step 4: Apply the Pythagorean Identity

We know that \(\sin^2 \theta + \cos^2 \theta = 1\), so:

\[5 (1) = 5\]

The expression simplifies to 5.

From the given options, the correct answer is 4. 5.