Diode (LED) forward voltage in series and parallel
You don't have enough voltage to bias them all fully on, therefore your diodes will all be off. There will be a small amount of current through them, and the voltages will be approximately equal across each one, but you won't see them light up (or if you do, they'll be dim). It won't be a fifth of 9V though, because some will drop in the resistor, too.

This method of many diodes in series with a single current-limiting resistor (or other current limit device) is actually quite common; you see it all the time in LED lightbulbs. Since you need fewer resistors (which waste some energy as heat) it means higher efficiency, and on top of that it's a lower cost since there are fewer parts.

For further reading, try the search term "Shockley diode equation". There is a mathematical relationship between diode current and voltage, it's just nonlinear.