You are heading in the right direction. If you wrap the essence of your code in a for loop that iterates over the files you need to process and change the hash access from an assignment to a += then you've done the input part. Generating the output is then a matter of two nested loops. Consider:

use strict;
use warnings;

my $file1 = <<END_FILE1;
0: 0,11 5,6 11,2
1: 1,3
3: 0,1 2,2 3,2
5: 3,5 6,1 8,16 9,1
END_FILE1

my $file2 = <<END_FILE2;
0: 0,10 4,19
2: 1,3 2,5 6,4
5: 6,10 9,3
END_FILE2

my %sites;

for my $source (\$file1, \$file2) {
    open my $inFile, '<', $source or die "Failed to open $source: $!\n
+";

    while (my $line = <$inFile>) {
        chomp $line;
        
        next if ! ($line =~ s/^([^:]+):\s*//);

        my $word = $1;

        for my $field (split ' ', $line) {
            my ($site, $count) = split /,/, $field;

            $sites{$word}{$site} += $count;
        }
    }
}


for my $word (sort {$a <=> $b} keys %sites) {
    print "$word: ";
    
    my $wordSites = $sites{$word};
    
    for my $site (sort {$a <=> $b} keys %$wordSites) {
        print "$site,$wordSites->{$site} ";
    }
    
    print "\n";
}
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Prints:

0: 0,21 4,19 5,6 11,2 
1: 1,3 
2: 1,3 2,5 6,4 
3: 0,1 2,2 3,2 
5: 3,5 6,11 8,16 9,4
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There are a few things you ought do to save yourself time in the future. First off, always use strictures (use strict; use warnings;). Use the three parameter version of open (you didn't did you?) and always test the result of file opens. Use lexical file handles (open my $infile ...).

Note the indentation and bracketing style I've used in my sample. It is pretty common in Perl circles and is probably worth adopting. There is a really good tool called Perl Tidy that is well worth getting if you are at all interested in generating consistently formatted code.

You have a good start on reading the first file. Now you just need to use the same hash when reading the second file, and do:

    $file1{$word}{$site} += $count;
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You should also start with use strict; and it will make sense to have your file reading logic in a subroutine that you call for each file, just to avoid repeating code unnecessarily:

use strict;

my %data;
my @filenames = ...;  # @ARGV or literal strings or whatever

for my $fname ( @filenames ) {
    open my $input, "<", $fname or die "$fname: $!";
    load_data( $input, \%data );
}

# doing stuff with %data is left as an exercise...

sub load_data
{
     my ( $fh, $href ) = @_;
     while ( <$fh> ) {
        next unless ( s/^(.*?):\s*// );
        my $word = $1;
        for my $field ( split ) {
            my ( $site, $count ) = split /,/, $field;
            $$href{$word}{$site} += $count;
        }
    }
}
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Look at the structure of your data. You want to sort a list of numbers where each list is associated with a unique key What do you think is the data structure you need to put the data into?
Something like:
%records{$number_before_colon => @list_of_numbers_seperated_by_commas}
So read each file splitting the result into an index and an array and add the array to a hash on the index.

while(<INFILE>){
   chomp;
   ($index,@record)=split/[:,]/;
   push @{$records{$index}},@record;
}
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for $index (sort{$a<=>$b}(keys (%records))){
        print $OUTFILE "$index: ",join(",",(sort{$a<=>$b}(@{$records{$
+index}}))),"\n";
}
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#!/usr/bin/perl
use strict;
use warnings;
my @files=qw(temp.data temp1.data temp2.data);
my ($file,$index, %records,$INFILE,$OUTFILE);
for $file (@files){
        open($INFILE,"<","$file")|| die "Failed to open $file: $!";
        while(<$INFILE>){
                my @record;
                chomp;
                ($index,@record)=split/[:,]/;
                push @{$records{$index}},@record;
        }
        close $INFILE;
}

open ($OUTFILE,">","newfile.data")|| die "Failed to open newfile.data:
+ $!";
for $index (sort{$a<=>$b}(keys (%records))){
        print $OUTFILE "$index: ",join(",",(sort{$a<=>$b}(@{$records{$
+index}}))),"\n";
}
close $OUTFILE
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