Is applying 5 volts to LED dangerous?
Different color LEDs are not the same.  The are made with different impurities.  And some colors (blue) were really hard to figure out.  So much so that the blue LED inventor was awarded the Nobel Prize!

Consequently, it should not be assume all LEDs operate at the same voltage and current.  As such, when driving an LED with a constant voltage source, derive the proper series resistance for each case. 

Example 1: 

Given a red LED which may have 1.8 volt drop and may need 20mAmps to operate driven by a 5 volt source, we find the proper series resistor to be...


  V = I * R 
  
  5 - 1.8 = 20mA * R 
  
  R = (5 - 1.8) / 0.020 
  
  R = 160 ohms


Example 2:

Given a blue LED which may have a 3.3 volt drop and may need 20mAmps to operate driven by a 5 volt source, we find the proper series resistor to be...


  V = I * R 
  
  5 - 3.3 = 20mA * R 
  
  R = (5 - 3.3) / 0.020 
  
  R = 85 ohms


Your specific LEDs may have different specifications.  The above are only examples.

Go here for more about calculating the proper LED series resistance.

In general, LEDs that are over driven will grow dimmer and not recover.