A tip:
Whenever initializing a variable to keep track of a product, initialize it to the first entry or factor.
//do not do this
int product = 0;
product *= intArray[0];
product *= intArray[1];
product *= intArray[2];
...
//do this
int product = intArray[0];
//or
int product = 1;
Also:
if (count == 5)
System.out.println("Sum = " + sum);
System.out.println("Product = " + product);
Java allows syntax for using the if statement implicitly with no braces, but only one statement following the if clause is counted in the implied "then" clause. If you use braces, you are being explicit and explicit is better.