untested. On unix grep can do exactly this.

my $MAX = 5;
local $_;
OUT: while ( defined ( $_ = <LOG> ) ){
  push @lines, $_;
  shift @lines if @lines > $MAX;
  if ( /bla bla/ ) {
    print @lines, $_;
    for ( 1 .. $MAX ) {
      last OUT unless defined ( $_ = <LOG> );
      print;
    }
  }
}
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