 Solution

Take a complete graph on vertices $a,b,c,d$ and add a fifth vertex $v$ joined only to $a$ and $b$. The minimum degree is two, which is less than $5/2$. The only nonadjacent pairs are $(v,c)$ and $(v,d)$, and each has degree sum $2+3=5$. Thus Ore's condition holds even though the minimum-degree condition fails. For example,is a Hamiltonian cycle in this graph.