I have to wake up earlier =). I've come with a similar solution redefining $/, but this time using split. Here is:

#!/usr/local/bin/perl
use strict;
use warnings;
use Data::Dumper;

my %hash;
local $/ = ">";
<DATA>; #Skip first ">"
while(<DATA>){
        my ($key,$value) = split /\n/, $_ , 2;
        $key =~ s/(\S+).*?$/$1/;
        $value =~ s/\n\>?//g;
        $hash{$key} = $value;
}

print Dumper \%hash;
__DATA__
>EP11110 (-)
TGCAATCACTAGCAAGCTCTC
GCTGCCGTCACTAGCCTGTGG
>EP40005 (+)
GGGGCTAGGGTTAGTTCTGGA
NNNNNNNNNNNNNNNNNNNNN
__OUTPUT__
$VAR1 = {
          'EP40005' => 'GGGGCTAGGGTTAGTTCTGGANNNNNNNNNNNNNNNNNNNNN',
          'EP11110' => 'TGCAATCACTAGCAAGCTCTCGCTGCCGTCACTAGCCTGTGG'
        };
[download]

Regards,
deibyz