AnomalousMonk: I enjoy your regexes! Anyway, here's another solution (am reading "all possible substrings" as "all possible substring matches"):

use Modern::Perl;

my @userDefined = qw(AAA AAC ACA CAA);
my $string      = 'AAAAA AAACACA CAACAAA';

foreach my $element (@userDefined) {
    my ( $found, $elemLen ) = ( 0, length $element );
    for ( my $i = 0 ; $i < length($string) - 2 ; $i++ ) {
        $found++
          if substr( $string, $i, $elemLen ) eq $element;
    }
    say "$element: $found";
}
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Output:

AAA: 5
AAC: 2
ACA: 3
CAA: 2
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