here a oneliner version (that skips tuple without range specification). Pay attention to windows double quotes

perl -nle "$x++ if 0==$.%4;$a[$x].=$_}{for(@a){next unless/Range/;s/ST
+/ST,/;/\s(\d+)(\w) - \d+(\w)\W/;$n=$1;for $l(qq($2)..qq($3)){print s/
+\(.*\)/$n$l, /r}}" add-data.txt

432 10TH ST, APT 2A, BROOKLYN NY 10598-6601
432 10TH ST, APT 2B, BROOKLYN NY 10598-6601
432 10TH ST, APT 3A, BROOKLYN NY 10598-6601
432 10TH ST, APT 3B, BROOKLYN NY 10598-6601
432 10TH ST, APT 4A, BROOKLYN NY 10598-6605
432 10TH ST, APT 4B, BROOKLYN NY 10598-6605
432 10TH ST, APT 5A, BROOKLYN NY 10598-6605
432 10TH ST, APT 5B, BROOKLYN NY 10598-6605
432 10TH ST, APT 5C, BROOKLYN NY 10598-6605
432 10TH ST, APT 5D, BROOKLYN NY 10598-6605
[download]

The trick is to read 3 lines at time (2 interesting plus the empty one in the middle) to build a longer line. Then with capturing parens you can grab the range to expand. See it deparsed:

perl -MO=Deparse -nle "$x++ if 0==$.%4;$a[$x].=$_}{for(@a){next unless
+/Range/;s/ST/ST,/;/\s(\d+)(\w) - \d+(\w)\W/;$n=$1;for $l(qq($2)..qq($
+3)){print s/\(.*\)/$n$l, /r}}" add-data.txt

BEGIN { $/ = "\n"; $\ = "\n"; }
LINE: while (defined($_ = readline ARGV)) {
    chomp $_;
    ++$x if 0 == $. % 4;
    $a[$x] .= $_;
}
{
    foreach $_ (@a) {
        next unless /Range/;
        s/ST/ST,/;
        /\s(\d+)(\w) - \d+(\w)\W/;
        $n = $1;
        foreach $l ("$2" .. "$3") {
            print s/\(.*\)/$n$l, /r;
        }
    }
}
-e syntax OK
[download]

L*