  Let $2 \le r < m$ and $g$ be positive integers. An $({r,m};g)$--graph} (or
biregular graph) is a graph with degree set ${r,m}$ and girth $g$, and an
$({r,m};g)$-cage (or biregular cage) is an $({r,m};g)$-graph of minimum order
$n({r,m};g)$. If $m=r+1$, an $({r,m};g)$-cage is said to be a semiregular cage.
  In this paper we generalize the reduction and graph amalgam operations from
M. Abreu, G. Araujo-Pardo, C. Balbuena, D. Labbate (2011) on the incidence
graphs of an affine and a biaffine plane obtaining two new infinite families of
biregular cages and two new semiregular cages. The constructed new families are
$({r,2r-3};5)$-cages for all $r=q+1$ with $q$ a prime power, and
$({r,2r-5};5)$-cages for all $r=q+1$ with $q$ a prime. The new semiregular
cages are constructed for r=5 and 6 with 31 and 43 vertices respectively.
