Well done. Now lets refine what you have.
First, your form is still setup wrong. You have two submits (which isn't an issue, but is unnecessary) and you close your form half way through the code. Try running your code and doing the print I posted earlier: see what it does and figure out what its doing.
Next, every time you load the calculation page, it will try to find $_POST['num1'] et all. Since someone might accidentally go to that page without going through the form first, if any of those post variables are not set, they'll get an error. So you want to first verify that they are set. Its commonly done via the function isset (which as it suggests, checks if a variable is set). Be sure to read through php.net... documenation will be your best friend! So you'll want to give your submit button a name (lets call it submit) and do something like this:
PHP Code:
if (isset($_POST['submit'])) {
$num1 = $_POST['num1'];
$num2 = $_POST['num2'];
$num3 = $_POST['num3'];
$num4 = $_POST['num4'];
$num5 = $_POST['num5'];
$a = $num1 + $num2 + $num3 + $num4 + $num5;
$b = $num1 - $num2 + $num3 + $num4 + $num5;
echo "The sum of the five numbers is ". $a;
echo "The difference of the five numbers is ". $b;
}
So it will check if you've actually submitted the form. That's obviously very weak checking though, but it gives you an idea of where to go from here.
Next, I don't see a doctype defined. That's very important, as it tells the page how to figure stuff out. Most people go for the HTML5 doctype these days, and I think its the simplest (and of course, the most future proof, for now). Read up on doctypes.
But great progress!