Delay() is 5 times too long

Rework without the delay between each byte, eg.

const int ledPin = 13;
byte input1;

void setup()
{
  Serial.begin(28800);
}

void loop()
{
  while (Serial.available())    // while data is received
  {
    input1 = Serial.read();
    if (input1 < 128)   // just a check that I don't receive random crap
      {
      Serial.write(input1);   // send the data back to check
      }
  }

// short delay *here* if you absolutely must

}