The number of points $\left(x,y\right)$ having integral coordinates lying inside the circle $x^2+y^2=25$ is $n$, then the value of $n$

The given circle is $x^2+y^2=25$

The points $\left(x,y\right)$ which satisfies the condition. $-4\le x\le 4,-4\le y\le 4$

The possible $x$ coordinates are $\left\{-4,-3,-2,-1,0,1,2,3,4\right\}$ and similarly the possible $y$ coordinates are $\left\{-4,-3,-2,-1,0,1,2,3,4\right\}$

There are 81 points are there which lies on the circle or inside the circle

The points which lies on the circle are 

$(\pm 4,\pm 4),(\pm 4,\pm 3)\text{ and }(\pm 3,\pm 4)$, 12 points

Therefore, the number of points which lies inside the circle is $n=81-12=\boxed{69}$