Help with basic LCD menu

I'm confused by dhenry's answer.

Your original question was how to show 5 screens by pushing one button?

This shows the general idea. It outputs to serial so you can test by just grounding pin 8 (to act as your switch).

const byte mySwitch = 8;  

// these "states" are what screen is currently being displayed.
typedef enum 
  {
  POWER_ON, COOLANT, INTAKE_SPEED, EXHAUST_FAN1, EXHAUST_FAN2,
  // add more here ...
  
  LAST_STATE  // have this last
  } states;

byte state = POWER_ON;

byte oldSwitch = HIGH;

void powerOn ()
  {
  Serial.println ("Welcome!");
  }
 
void showCoolant ()
  {
  Serial.println ("Coolant level = x");
  }
  
void showIntakeSpeed ()
  {
  Serial.println ("Intake speed = x");
  }
  
void showExhaustFan1 ()
  {
  Serial.println ("Exhaust Fan 1 = x");
  }
  
void showExhaustFan2 ()
  {
  Serial.println ("Exhaust Fan 2 = x");
  }
  
void setup ()
  {
  pinMode (mySwitch, INPUT_PULLUP);
  Serial.begin (115200);
  powerOn ();
  }  // end of setup
  
void loop ()
  {
  byte switchValue = digitalRead (mySwitch);
  
  // detect switch presses
  if (switchValue != oldSwitch)
    {
    delay (100);   // debounce

    // was it pressed?
    if (switchValue == LOW)
      {
      state++;      // next state
      if (state >= LAST_STATE)
        state = COOLANT;  
      
      switch (state)
        {
        case POWER_ON:     powerOn ();         break;
        case COOLANT:      showCoolant ();     break;
        case INTAKE_SPEED: showIntakeSpeed (); break;
        case EXHAUST_FAN1: showExhaustFan1 (); break;
        case EXHAUST_FAN2: showExhaustFan2 (); break;
        }  // end of switch
      }  // end of switch being pressed
      
    oldSwitch = switchValue;  
    } // end of switch changing state
    
  }  // end of loop