To start... this should be in the void loop() not the void setup () else it only runs once on boot

AND it is not properly written/formatted with brackets {} so it would give a compiling error in the first place.

  
if (digitalRead(5) == HIGH) {  // if pin 5 enjoyed a high level voltage
    RemoteXY.led_1 = 255;  // then turn on red light
 } else {   // else
    RemoteXY.led_1 = 0;  // turn off red
}

RemoteXY include library          //
//////////////////////////////////////////////

// RemoteXY select connection mode and include library
#define REMOTEXY_MODE__ESP8266_HARDSERIAL_CLOUD

#include <RemoteXY.h>

// RemoteXY connection settings
#define REMOTEXY_SERIAL Serial
#define REMOTEXY_SERIAL_SPEED 9600
#define REMOTEXY_WIFI_SSID "AirTies_Air5650-1"
#define REMOTEXY_WIFI_PASSWORD "kzekih102030"
#define REMOTEXY_CLOUD_SERVER "cloud.remotexy.com"
#define REMOTEXY_CLOUD_PORT 6376
#define REMOTEXY_CLOUD_TOKEN "4644ff9d2ef7698939217c10191b3a4b"

// RemoteXY configurate 
#pragma pack(push, 1)
uint8_t RemoteXY_CONF[] =
  { 255,1,0,25,0,95,0,13,158,1,
  70,24,32,20,18,18,48,36,2,1,
  0,33,45,18,18,2,31,88,0,129,
  0,46,87,9,2,22,68,105,122,97,
  121,110,32,75,90,0,66,0,8,5,
  4,40,2,26,66,64,8,45,4,45,
  2,26,129,0,16,66,13,5,17,73,
  83,73,0,129,0,16,10,12,5,17,
  78,69,77,0,67,4,16,15,20,5,
  2,26,11,67,4,16,73,20,5,2,
  26,11 };
 
// this structure defines all the variables and events of your control interface
struct {

    // input variables
  uint8_t button_1; // =1 if button pressed, else =0

    // output variables
  uint8_t led_1; // led state 0 .. 1
  int8_t level_1; // =0..100 level position
  int8_t level_2; // =0..100 level position
  char text_1[11];  // string UTF8 end zero
  char text_2[11];  // string UTF8 end zero

    // other variable
  uint8_t connect_flag;  // =1 if wire connected, else =0

} RemoteXY;
#pragma pack(pop)

/////////////////////////////////////////////
//           END RemoteXY include          //
/////////////////////////////////////////////

#define PIN_BUTTON_1 5

void setup()
{
  RemoteXY_Init ();
 
  pinMode (PIN_BUTTON_1, OUTPUT);
 
  if (digitalRead(5) == HIGH) // if pin 5 enjoyed a high level voltage
    RemoteXY.led_1= 255;   // then turn on red light
  else                        // else
    RemoteXY.led_1= 0;     // turn off red
   
  // TODO you setup code
 
}

void loop()
{
  RemoteXY_Handler ();
 
  digitalWrite(PIN_BUTTON_1, (RemoteXY.button_1==0)?LOW:HIGH);
 
  // TODO you loop code
  // use the RemoteXY structure for data transfer
  // do not call delay()

I'm writing from your examples, but I'm getting an error

Hello, this forum is here to assist you, not write your code for you  

Perhaps we can figure out what error you are getting and assist with that?

I would be very grateful if you could write a short code example. I'm writing from your examples, but I'm getting an error. I would appreciate it if you write and send the full code in the form of Arduino Nano + wifi Module+1 output+1 input.

Thank you