Controller that supports multiple LCDs, ideally up to 5
I'm assuming when you say controller, you mean a microcontroller, the confusion only arises because LCDs themselves have controllers. 

The answer is yes, the STM32F103RE would work for what you want to do. It's compatible with the .net micro framework and it has plenty of options to run serial displays on, be it SPI, I2C, or asynchronous serial. Perhaps a display like this one.

Whichever display you go with, try to find one with onboard memory, you'll save yourself some headaches that way.