$$\begin{gathered} \text{Simplify} \\ \mathrm{} \end{gathered}$$

$5\times [14÷13\times \{13\times 14÷(14\times 14)\left\}\right]$

The correct option is 5.

To simplify the given numerical expression, we follow the standard order of operations (BODMAS/PEMDAS), solving from the innermost parentheses outwards:

$5\times [14÷13\times \{13\times 14÷(14\times 14)\left\}\right]$

Step 1: Simplify the innermost parenthetical expression (14 × 14):

Notice that inside the curly brackets, we have $13\times 14÷(14\times 14)$. Writing the division as a fraction:

$\frac{13\times 14}{14\times 14}=\frac{13}{14}$

Step 2: Substitute this result back into the expression inside the square brackets:

$14÷13\times \frac{13}{14}$

Converting the division to multiplication by the reciprocal:

$\frac{14}{13}\times \frac{13}{14}=1$

Step 3: Perform the final multiplication with the outer number:

$5\times 1=5$

Thus, the simplified value of the given expression is 5.