Hi William!
You can create this type of shipping system by using flate-rate shipping and manipulating the weight of your products. For example, make the weight of all your products 1lb. Then set up a shipping rate for 0-4 lb to be Standard Shipping, and then you can create a second rate for 5lb and up to be the more expensive shipping. Once that 5th product is added to the cart the weight will be 5lb as well, so it will present the more expensive rate to your shopper. Here is our Doc on Shipping Rates if you need a refresh on how to set it up!
Cheers!