Evaluate
` ( 5 sin 66 ^(@))/( cos 24 ^(@)) -( 2 cot 85^(@))/(tan 5^(@))`

Answer

To evaluate the expression \( \frac{5 \sin 66^\circ}{\cos 24^\circ} - \frac{2 \cot 85^\circ}{\tan 5^\circ} \), we can follow these steps:

### Step 1: Rewrite the expression using trigonometric identities
We know that:
- \( \cos 24^\circ = \sin(90^\circ - 24^\circ) = \sin 66^\circ \)
- \( \tan(90^\circ - \theta) = \cot \theta \)

Thus, we can rewrite the expression as:
\[ \frac{5 \sin 66^\circ}{\sin 66^\circ} - \frac{2 \cot 85^\circ}{\cot 85^\circ} \]

### Step 2: Simplify the fractions
Now, we can simplify each term:
\[ \frac{5 \sin 66^\circ}{\sin 66^\circ} = 5 \]
and
\[ \frac{2 \cot 85^\circ}{\cot 85^\circ} = 2 \]

### Step 3: Combine the results
Now we can combine the results from the simplifications:
\[ 5 - 2 = 3 \]

### Final Answer
Thus, the value of the given expression is:
\[ \boxed{3} \]

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