I'm trying to compute the genus of the normalization of the curve: $y^5=x(x-1)(x-2)$ Now I calculate the ramification points of the projection x: they are $(0,0),(1,0),(2,0)$ and they are of ramification order 5, and possibly ramification points at the infinite point $(1:0:0)$.
Now the curve is singular at $(1:0:0)$, and after a long blow up computation I found another ramified point of degree 5. The Riemann Hurwitz formula then gives that the genus is 4.
EDIT: As suggested below the genus-degree formula has a correction term for singularities. The curve has one singularity at infinity: $(1:0:0)$. The equation for a neighborhood around this point is given by $y^5-z^2x^2-3z^3x-2z^4$. Following the procedure for calculating the multiplicty of a singular point outlined in the link below I find that it is equal to 2. Hence the genus of the curve is $g(C)=(d-1)d/2-r(r-1)/2=(5-1)(4-1)/2-2(2-1)/2=6-1=5$.
Again however the genus does not agree with the computation with ramification points. Moreover even if the ramification at infinity is different this can only decrease the genus of the curve to be smaller than 4.