  The low-energy limit of the massless two-loop five-point amplitudes for both
type IIA and type IIB superstrings is computed with the pure spinor formalism
and its overall coefficient determined from first principles. For the type IIB
theory, the five-graviton amplitude is found to be proportional to its
tree-level counterpart at the corresponding order in $\alpha'$. Their ratio
ties in with expectations based on S-duality since it matches the same modular
function $E_{5/2}$ which relates the two-loop and tree-level four-graviton
amplitudes. For R-symmetry violating states, the ratio between tree-level and
two-loop amplitudes at the same $\alpha'$-order carries an additional factor of
$-3/5$. Its S-duality origin can be traced back to a modular form derived from
$E_{5/2}$.
