Maximum current draw for the 5" Nextion (backlight @ 100%) is?410mA?
Arduino Nano ~20mA
Si5351 (all outputs enabled) ~22mA
Assuming 13.8V input, there's over 4W of thermal power to be dissipated. As Allison already explained, whatever IC you'll use it'll need a heatsink.
Also, try to keep the heat away from the Si5351 oscillator crystal as it would generate frequency drift.
