A combination of the already recommended flip-flop inside a grep along with a join and a split breaks the file into records nicely.

knoppix@Microknoppix:~$ perl -E '
> open my $fh, q{<}, \ <<EOD or die $!;
> dsfiu
> =begin
> line1
> line2
> =end
> wwefgwf
> werfwef
> =begin
> line3
> line4
> line5
> =end
> sadfwfe
> dfbsdfbsfd
> EOD
> 
> @recs =
>    split m{(?<==end\n)(?==begin)},
>    join q{},
>    grep { m{=begin} .. m{=end} }
>    <$fh>;
> 
> print do { local $" = qq{**********\n}; qq{@recs} };'
=begin
line1
line2
=end
**********
=begin
line3
line4
line5
=end
knoppix@Microknoppix:~$
[download]

I hope this is helpful.