Q: How do i connect my personal hotspot on my iphone 5s to my HP  TOUCHSCREEN LAPTOP SO I CAN COMPLETE SET UP AND USE INTERNET.

The "network security key" is another name for wi-fi password. What you need to enter in your laptop is the Wi-Fi Password shown in the iPhone's Settings App. Open Settings then tap Cellular then Personal Hotspot. There is a picture of it (with the password blurred out) -- 2nd picture from the top in iOS: Understanding Personal Hotspot

I'm hoping you are already aware that using that feature with a laptop connected is likely to result in very substantial data usage on your cellular data plan.