Simplify the following expression:
$$5\times [14÷13\times \{13\times 14÷(14\times 14)\}]$$

Following the BODMAS rule, we solve the expression step-by-step starting from the innermost brackets:
Given expression:

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

Step 1: Solve the innermost parentheses $(14\times 14)$:

$$14\times 14=196$$

The expression becomes:

$$5\times [14÷13\times \{13\times 14÷196\}]$$

Step 2: Solve the operations inside the curly braces $\{\}$, performing division first or rewriting as a fraction:

$$\{13\times \frac{14}{196}\}=\{13\times \frac{1}{14}\}=\{\frac{13}{14}\}$$

The expression becomes:

$$5\times [14÷13\times \frac{13}{14}]$$

Step 3: Solve the operations inside the square brackets $[]$ from left to right:

$$14÷13=\frac{14}{13}$$

Now multiply by $\frac{13}{14}$:

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

The expression becomes:

$$5\times 1=5$$

Therefore, the simplified value is $5$.