GrandFather already identified the problem in your code; in case you'd like to extend your program to other numerals (1,2,3 - as noted by gangabass), there's another variant:

use strict;
use warnings;

my $dates = '5th April -  12th April xxxx,
ssss, 3rd May   -  23th May zzz!
1st June-2nd June,  ddd';

my $subexp = qr{
                 (?:-\s*)?           # may be we hit the second term
                 \d+ (?:st|nd|rd|th) # the day
                 \s+\w+\s*           # the month  
               }x;
     
my @hits = $dates =~ /$subexp $subexp/xg;
print join "\n", @hits;
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Regards

mwa