Controlling multiple servos independently from serial monitor inputs

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Loop() loops very quickly, thousands of times per second. I think that you are reading the ADC and updating the servos way too often. Try this code and see if it works better.

#include <Servo.h>

Servo servo1;
Servo servo2;
Servo servo3;
Servo servo4;
Servo servo5;

void setup()
{
   servo1.attach(1);
   servo2.attach(2);
   servo3.attach(3);
   servo4.attach(4);
   servo5.attach(5);;
}

void loop()
{
   static unsigned long timer = 0;
   unsigned long interval = 100;
   if (millis() - timer >= interval)
   {
      timer = millis();
      servo1.write(analogRead(A0) / 6);
      servo2.write(analogRead(A1) / 6);
      servo3.write(analogRead(A2) / 6);
      servo4.write(analogRead(A3) / 6);
      servo5.write(analogRead(A4) / 6);
   }
}

How are the servos powered?