How to calculate the oxidation number of sulfur in H2SO5?
$\ce {H_2SO_5}$ has an oxygen-oxygen bond. This means that two of the five oxygen atoms have an oxidation number of $-1$. Same case as in $\ce{H2O2}$.

$$2\cdot (+1) + 1\cdot(x) + 3\cdot(-2) + 2\cdot (-1) = 0\\2 + x - 6 - 2 = 0\\
x = +6$$

You have 3 oxygens with oxidation number $-2$ and 2 oxygen atoms with $-1$.