I would say there is no need to worry about date rollover, because the collating sequence for YYYYMMDD is already in the right order. Therefore:

opendir my $dh, "path/images" or die $!;
my $min = '2005-04-05';
my $max = '2005-05-05';
my $found = '';
for my $file ( grep !/^\./, readdir $dh ) {
    unless ( $file =~ /^((\d){4}\-(\d){2}-(\d){2}\.jpg)$/ ){
        warn "Rejected filename $file";
        next;
    if ( ( $file le $max ) and ( $file ge $min ) and ( $file gt $found
+ ) ) {
        $found = $file;
    }
}
closedir $dh;
print "$found\n";
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