  Let $\bar{p}(n)$ denote the number of overpartitions of $n$. It was
conjectured by Hirschhorn and Sellers that $\bar{p}(40n+35)\equiv 0\ ({\rm
mod\} 40)$ for $n\geq 0$. Employing 2-dissection formulas of quotients of theta
functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating
function for $\bar{p}(40n+35)$ modulo 5. Using the $(p, k)$-parametrization of
theta functions given by Alaca, Alaca and Williams, we give a proof of the
congruence $\bar{p}(40n+35)\equiv 0\ ({\rm mod\} 5)$. Combining this congruence
and the congruence $\bar{p}(4n+3)\equiv 0\ ({\rm mod\} 8)$ obtained by
Hirschhorn and Sellers, and Fortin, Jacob and Mathieu, we give a proof of the
conjecture of Hirschhorn and Sellers.
