Without any error checking this works for you sample:

use warnings;
use strict;

my $rawdata = qq|
<COLUMNS>~ItemName1~ItemName2~ItemName3~ItemName4~ItemName5~</COLUMNS>
<DATA>~Apple~Orange~Banana~Pear~Watermelon~</DATA>
<DATA>~Blue~Red~Yellow~Brown~Purple~</DATA>
<DATA>~Uno~Dos~Tres~Cuatro~Cinco~</DATA>
|;

my @datalines = grep {length} split "\n",$rawdata;
my @listings;

my $header;
foreach my $line (@datalines) {
    if ($line =~ /^<COLUMNS>(.+)<\/COLUMNS>/) {
        $header = $1;
    } elsif ($line =~ /^<DATA>(.+)<\/DATA>/) {
        push(@listings, $1);
    }
}

my %hoa;

my @keys = grep {length} split '~', $header;
for my $listing (@listings) {
    my @list = grep {length} split '~', $listing;
    
    push @{$hoa{$keys[$_]}}, $list[$_] for 0..$#keys;
}

print "$_ => @{$hoa{$_}}\n" for sort keys %hoa;
[download]

Prints:

ItemName1 => Apple Blue Uno
ItemName2 => Orange Red Dos
ItemName3 => Banana Yellow Tres
ItemName4 => Pear Brown Cuatro
ItemName5 => Watermelon Purple Cinco
[download]