You don't really need any module other than core Time::Local.

use Time::Local;
use 5.010;

my ( $month, $year ) = ( gmtime($^T) )[ 4, 5 ];
my @month_days = ( 5, 16, 20 );

say timegm( 59, 59, 23, $_, $month, $year ) for @month_days;
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In addition, that sort of simplifies things, doesn't it?

Update: Linkified Time::Local