There are a lot of much more powerful boards available (especially if you move from ATmega to ARM). I'm partial to the Teensy boards myself but Adafruit also makes some nice ARM-based boards. For example, I'm currently developing a multi-user, Arduino-compatible Unix-ish OS on one of the latter (48MHz ARM, 256kB flash, 32kB SRAM) and it runs great.

(No affiliation to either of those companies)

There are a lot of much more powerful boards available (especially if you move from ATmega to ARM). I'm partial to the Teensy boards myself but Adafruit also makes some nice ARM-based boards. For example, I'm currently developing a multi-user, Arduino-compatible Unix-ish OS on one of the latter (48MHz ARM, 256kB flash, 32kB SRAM) and it runs great. Honestly, controlling 5 non-graphical LCDs over I²C is should be easily doable on an Uno but if you need more power there are lots of options available.

(No affiliation to either of those companies)