If $a\ast b=ab+b-a$, what is the value of $c$ such that $c\ast (2\ast 5)=97$?

First, let's calculate the numerical value inside the parentheses by substituting $a=2$ and $b=5$ into the given function rule:
$$2\ast 5=(2\times 5)+5-2$$

$$2\ast 5=10+5-2=13$$

Now, substitute this result back into the main equation, setting up $c\ast 13=97$:

$$c\ast 13=(c\times 13)+13-c=97$$

$$13c+13-c=97$$

$$12c+13=97$$

$$12c=97-13$$

$$12c=84$$

$$c=\frac{84}{12}=7$$