This should be trivial

T'is trivial if you use the right tool:

$ham = "spam\tspam\tspam\t\tyam\tclam";;
@jam = split /\t+/, $ham;;

print "@jam";;
spam spam spam yam clam
[download]

1. Text::CSV and its ilk - You are dealing with large delimited data files, so why not use a module designed to handle those?

2. If you have a line in memory and you know you want to get the 1st, 4th and 5th terms, why not just grab those terms?

   #!/usr/bin/perl
   use strict;
   use warnings;
   
   my $ham = "spam\tspam\tspam\t\tyam\tclam";
   my @jam;
   for my $i (0, 3, 4) {
       push @jam, $ham =~ /(?:[^\t]*\t){$i}([^\t]*)/;
   }
   
   print join("\n", '**', @jam, '**', '');
   [download]

   You could even code that into a single expression if you only wanted to run it once.

Is there NO way to capture all the matches to a numerically quantified subexpression?

This should be trivial, yet it seems to be impossible.

^†Actually, since 5.10, the number of capturing parens is an upper bound, due to the (?|) construct.

How about using variables to turn confusion to clarity? Better yet, go to the library and borrow Perl Best practices to see why '\A' is better than \$'. spreading out your regex and adding comments, helps, too.

my $ham = "spam\tspam\tspam\tyam\tclam";
my $word    = qr{[^\t]+};
my $sep     = qr{\t};
my $capture = qr{($word)};
my (@jam ) = ($ham =~ m{\A                 # enforce beginning of stri
+ng
                         $word $sep        # skip first word and separ
+ator
                         $word $sep        # and the second
                         $capture $sep     # capture next two words
                         $capture $sep     # skip the separators
                         $word             # skip a word
                        \z                 # and then it's the end of 
+the string
                       }xms);
print join("\n", '**', @jam, '**', '');
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Using the debugger helps, too ... Along the way I noticed your string has a double tab '\t\t', but you only ever accept single tabs; You specify end of string '$', when there's still another word to go.

But you're doing too much work. You could split() on '\t' and select only the components you want. If it's the 3rd % 4th ...

my @jam = ( spit "\t", $ham )[2,3];
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If you do need to use a regex, do you need to check whether there is a word after your capture? Do you need to enforce there is nothing after that last word? Simplify your regex for greater happiness.

Something like:

my $ham = "spam\tspam\tspam\t\tyam\tclam";
my @jam;
$ham =~ s/^[^\t]*\t[^\t]*((?:\t[^\t]*){3})\t[^\t]*$/push @jam,(split "
+\t",$1);$1/eg;

print join("\n", '**', @jam, '**', '');
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maybe?

Is there NO way to capture all the matches to a numerically quantified subexpression?

Of course there is:

use v6;
if "abc" ~~ /(.)+/{
    say $0.join(", ");
}
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In Perl 6, quantifying a capturing group or atom just results in an array of Match objects.

Thanks. Not sure whether Perl 6 is an option, but I'll take a look.

my $ham = "spam\tspam\tspam\t\tyam\tclam";

my @jam = ($ham =~ (m/^[^\t]+\t[^\t]+\t([^\t]+)(\t\t)([^\t]+)\t[^\t]+$
+/));

print join("\n", '**', @jam, '**', '');
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**
spam

yam
**
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my ($col1, $col2) = (split(/\t/, $ham))[2,4] ;
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use strict;
use warnings;
my $ham = "spam\tspam\tspam\t\tyam\tclam";
my @foo;
my @jam = ($ham =~ (m/^[^\t]*\t[^\t]*(?:\t([^\t]*)(?{push @foo, $^N}))
+{3}\t[^\t]*$/));
print join("\n", '**', @jam, '**', '');
print join("\n", '**', @foo, '**', '');
[download]

There are a couple of issues with that code, but the OP made it clear he only want a yes/no answer. I was going to post something of the kind, but it's not nearly as good as BrowserUk's solutions.