Reading an LED data sheet, voltage drop and supply voltage in an LED ring
The 2.8 to 3.4V is a typical operating voltage range for a white LED. It will have this rated voltage over it when running at the rated current.
The resistor value is calculated incorrectly. The false assumption is that all the 5V will be over the resistor, but it is not, since there will be 2.8V to 3.4V over the LED, so only the remaining voltage is over the resistor.
And you should not simply use the assumption that LEDs have always the maximum value of 3.4V over them, and calculate the resistance based on that, since the LEDs could just as well have the minimum value and then the current would exceed the nominal 60mA value and it can be over 80mA.