If $v$ and $c$, respectively, denote the number of vowels and the number of consonants in $\text{ANTIDISESTABLISHMENTARIANISM}$, then what is the value of $\frac{(c-v)\times c}{5v-4}$?

Let's count the vowels ($v$) and consonants ($c$) in the word:
$\text{A N T I D I S E S T A B L I S H M E N T A R I A N I S M}$

Vowels ($v$):
A, I, I, E, A, I, E, A, I, A, I (Count = 11)

Consonants ($c$):
N, T, D, S, S, T, B, L, S, H, M, N, T, R, N, S, M (Count = 17)

Let's double check the total letters: $11+17=28$ letters.
Now, substitute $v=11$ and $c=17$ into the given expression:

$$\text{Value}=\frac{(c-v)\times c}{5v-4}$$

$$\text{Value}=\frac{(17-11)\times 17}{5(11)-4}=\frac{6\times 17}{55-4}=\frac{102}{51}=2$$