by reading the lines five at a time and pulling the user number out of the first one:

use warnings;
use strict;
use Data::Dump::Streamer;

my %records;

while (! eof (DATA)) {
    my $line1 = <DATA>;

    next unless defined $line1 and $line1 =~ /^\s1/;

    $_ = <DATA> for my ($line2, $line3, $line4, $line5);
    my $id = substr $line1, 9, 5;

    $records{$id} = [$line1, $line2, $line3, $line4, $line5];
}

Dump (\%records);

__DATA__
 10101ABC000019101L0001374686047S30339  GA   &DOE    C080229CR7  7    
+00244   0000001 000000000
 2          CR7            000            060714Q                     
+        Y   0000000000 000
 3                              00030339                           3JO
+HN DOE               36
 423 MAIN STREET  ATLANTA                GA 30339
 5                                                          +000000000
+0080226I   052461  05241961

 10101ABC000029102 N                 D                                
+3658 MAIN STREET
 2                                ATLANTA                       GA3033
+9                           0001
 3JOHN DOE                                        05241961INDV37468604
+7S
 4
 5
[download]

Prints:

$HASH1 = {
           "00001" => [
                        " 10101ABC000019101L0001374686047S30339  GA   
+&DOE    C080229CR7  7    00".
    "244   0000001 000000000\n",
                        " 2          CR7            000            060
+714Q                       ".
    "      Y   0000000000 000\n",
                        " 3                              00030339     
+                      3JOHN".
    " DOE               36\n",
                        " 423 MAIN STREET  ATLANTA                GA 3
+0339\n",
                        " 5                                           
+               +00000000000".
    "80226I   052461  05241961\n"
                      ],
           "00002" => [
                        " 10101ABC000029102 N                 D       
+                         36".
    "58 MAIN STREET\n",
                        " 2                                ATLANTA    
+                   GA30339 ".
    "                          0001\n",
                        " 3JOHN DOE                                   
+     05241961INDV374686047S".
    "\n",
                        " 4\n",
                        " 5\n"
                      ]
         };
[download]

Note that I edited the second record to give it a unique id as described and that I restored what appeared to be a missing space in front of the first line of the first record.