Number of integral values of b for which the tangent parallel to line $y=x+1$ that can be drawn to the hyperbola $\frac{x^2}{5}-\frac{y^2}{b^2}=1$ is _________.

Equation of tangent hyperbola $\frac{x^2}{5}-\frac{y^2}{b^2}=1$ having slope m is $y=mx\pm \sqrt{a^2{m}^2-b^2}$ Or $y=x\pm \sqrt{5-b^2}$  
Comparing it with $y=x+1,$ We get $b^2=1,4$

$\therefore b=\pm 1,\pm 2$
Thus, four integral values of b are possible.