Ah, so the fields you want to look at are
for($i=1; $i<=5; $i++)
{
$gamenum = $_POST['gamenum'.$i];
$homescore = $_POST['homescore'.$i];
$visitorscore = $_POST['visitorcore'.$i];
...do stuff with $game, $homescore, and $visitorscore...
}
That does not check that the posted variables are actually present.
$gamenum = isset($_POST['gamenum'.$i]) ? (int)$_POST['gamenum'.$i] : 0;
(where the (int) is to force the value to be an integer) would be better; that's assuming that replacing missing fields with zero is appropriate.