  In this paper we obtain $(q+3)$--regular graphs of girth 5 with fewer
vertices than previously known ones for $q=13,17,19$ and for any prime $q \ge
23$ performing operations of reductions and amalgams on the Levi graph $B_q$ of
an elliptic semiplane of type ${\cal C}$. We also obtain a 13-regular graph of
girth 5 on 236 vertices from $B_{11}$ using the same technique.
