Answer
See the picture below
Work Step by Step
In order to graph the function, we have to calculate some points on the curve:
If x=-1 $\log_{5}(-1+1)$ diverges to $-\infty$
If x=0 $f(x)=\log_{5}(0+1)=0$
If x=1 $f(x)=\log_{5}(1+1)=0.4307$
If x=4 $f(x)=\log_{5}(4+1)=1$
If x=24 $f(x)=\log_{5}(24+1)=2$
By connecting these points, we can plot the curve.