Effect of LEDs in series instead of parallel with resistors
No. No. No. The current you get with no resistors will be very hard to predict, and will only by the greatest of chances be what you want (and small variations in the 5V and temperature will greatly affect whatever current you happen to get). 

Use one resistor per LED and be safe. 

You could put them in series and use a single resistor but the supply voltage should be more like like 9V in that case (and the resistor value calculated accordingly).