If $8\$3=32$ and $6\$4=30$, then $5\$4=?$

The correct option is 25.

To solve this puzzle, we need to determine the mathematical pattern represented by the symbol $\$$ using the given examples.

Let's analyze the first equation:

$8\$3=32$

We can achieve 32 by multiplying 8 by the number that is 1 greater than 3, which is 4:

$8\times (3+1)=8\times 4=32$

Now, let's verify this rule with the second equation:

$6\$4=30$

Using the same pattern, multiply 6 by the number that is 1 greater than 4, which is 5:

$6\times (4+1)=6\times 5=30$

The pattern holds true for both given equations. The operation $A\$B$ follows the formula:

$A\$B=A\times (B+1)$

Now, apply this rule to calculate $5\$4$:

$5\$4=5\times (4+1)$

$5\$4=5\times 5=25$

Therefore, the value of $5\$4$ is 25.