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

Let's count the total number of 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 are $\text{A, E, I, O, U}$:

1. A
2. I
3. I
4. E
5. A
6. I
7. E
8. A
9. I
10. A
11. I

Total number of vowels ($v$) = $11$.

Total number of letters in the word is $28$.
Therefore, the number of consonants ($c$) = $28-11=17$.

Now, substitute $v=11$ and $c=17$ into the given expression:

$$\frac{(c-v)\times c}{5v-4}=\frac{(17-11)\times 17}{5(11)-4}$$

$$\frac{6\times 17}{55-4}=\frac{102}{51}=2$$