The was nothing requiring date math in the OP, but DateTime also does time math. Since the OP is dealing with durations, she'd need DateTime::Duration.

Unfortunately, it doesn't produce the result one would expect because DateTime(::Duration) realises that not every minute has 60 seconds. Some are longer due to leap seconds.

use strict;
use warnings;

use DateTime::Duration qw( );

my @times = qw( 5:21 8:01 5:37 7:19 5:46 7:44 6:43 7:17 8:02 6:50 7:54
+ 8:44 );

my $dur = DateTime::Duration->new();
for my $time (@times) {
   my ($mins, $secs) = split(/:/, $time);
   $dur += DateTime::Duration->new(
      minutes => $mins,
      seconds => $secs,
   );
}

printf("%s hours, %s minutes, %s seconds\n",
   $dur->in_units(qw( hours minutes seconds ))
);
[download]

1 hours, 19 minutes, 378 seconds
[download]

From the docs, the only conversions possible are:

• years ⇔ months
• weeks ⇔ days
• hours ⇔ minutes
• seconds ⇔ nanoseconds

Now, you can use a reference datetime to determine minute length.

...

my $dur2 = do {
   my $ref = DateTime->new(
      year => 2006, month => 1, day => 1,
      hour => 0, minute => 0, second => 0,
      time_zone => 'UTC',
   );
   $ref + $dur - $ref
};

printf("%s hours, %s minutes, %s seconds\n",
   $dur2->in_units(qw( hours minutes seconds ))
);

my $dur3 = do {
   my $ref = DateTime->new(
      year => 2005, month => 12, day => 31,
      hour => 23, minute => 59, second => 59,
      time_zone => 'UTC',
   );
   $ref + $dur - $ref
};

printf("%s hours, %s minutes, %s seconds\n",
   $dur3->in_units(qw( hours minutes seconds ))
);
[download]

1 hours, 19 minutes, 378 seconds
1 hours, 25 minutes, 18 seconds   # All of the minutes had 60 seconds.
1 hours, 25 minutes, 19 seconds   # One of the minutes had 61 seconds.
[download]

Update: Added example where leap seconds affect the result.