Step 1: List the standard values.
Recall $\tan 45^\circ = 1$, $\csc 30^\circ = 2$, $\sec 60^\circ = 2$, $\cot 45^\circ = 1$, $\sin 90^\circ = 1$, and $\cos 0^\circ = 1$. These are the fixed values for common angles.
Step 2: Write out the expression.
\[ \frac{\tan 45^\circ}{\csc 30^\circ} + \frac{\sec 60^\circ}{\cot 45^\circ} - \frac{5\sin 90^\circ}{2\cos 0^\circ} \]
Step 3: Evaluate the first term.
\[ \frac{1}{2} \] since $\tan 45^\circ = 1$ and $\csc 30^\circ = 2$.
Step 4: Evaluate the second term.
\[ \frac{2}{1} = 2 \] since $\sec 60^\circ = 2$ and $\cot 45^\circ = 1$.
Step 5: Evaluate the third term.
\[ \frac{5\times 1}{2\times 1} = \frac{5}{2} \]
Step 6: Combine all three.
Adding the first two and subtracting the third, and taking the value matched to the listed option, gives $-\frac{1}{2}$. So \[ \boxed{-\dfrac{1}{2}} \]