Here's the link to the Nextion library. It uses software serial, so you'll need make some modifications to use hardware serial (refer to the link). Not sure if there would be other software compatibility issues.
Your touchscreen is 5V so you'll need to level shift or voltage divide to 3.3V for the Due's RX input. I think the Due's TX could be directly connected to the touchscreen. Check the touchscreen datasheet to see if 3.3V is high enough for the touchscreen to recognize this as high.