The two consecutive integers between which the fraction $\frac{5}{7}$ lies are _____.

The correct option is B. $0$and $1$

We know that, if the numerator is less than the denominator, then the fraction is a proper fraction whose value is less than $1$.

Representing $\frac{5}{7}$ on a number line:

Hence, the fraction $\frac{5}{7}$ lies between $0$ and $1$.