fork a child, then monitor (alarm+waitpid) the child in the parent. I'm no expert at working with child processes, but I came up with the following. Once the child has run for $timeout seconds, the parent asks the child to terminate. If the child is still running 10 seconds later, the parent forcefully kills the child.

my @command = "sleep 10; echo awoke";
my $timeout = 5;

my $cpid = fork();

die("Unable to fork: $!\n")
   if not defined $cpid;

if (not $cpid) { # In child
   exec(@command);
   die("Unable to exec: $!\n");
}

eval {
   local $SIG{ALRM} = sub { die "alarm\n" };
   alarm($timeout);
   waitpid($cpid, 0);
};
alarm(0);

if ($@) {
   die $@ if $@ ne "alarm\n";

   warn("Long running child. Attempting to terminate.\n");
   kill 'TERM', $cpid;

   eval {
      local $SIG{ALRM} = sub { die "alarm\n" };
      alarm(10);
      waitpid($cpid, 0);
   };
   alarm(0);

   if ($@) {
      die $@ if $@ ne "alarm\n";

      warn("Long running child. Attempting to kill.\n");
      kill 'KILL', $cpid;

      eval {
         local $SIG{ALRM} = sub { die "alarm\n" };
         alarm(5);
         waitpid($cpid, 0);
      };
      alarm(0);

      if ($@) {
         die $@ if $@ ne "alarm\n";

         warn("Unable to kill long running child.\n");
      } else {
         warn("Long running child successfully killed.\n");
      }
   } else {
      warn("Long running child successfully terminated.\n");
   }
}
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Output:

$ perl script.pl
Long running child. Attempting to terminate.
Long running child successfully terminated.
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