Slightly more in depth: if you share a resistor among multiple LEDs, like this:

It will work in a perfect, simulated world, but not this one. When the LEDs glow, they warm up. As they warm up, they drop in impedance, taking more current for a given voltage. They all have the same voltage applied to them, because they're directly in parallel, so any LED which has lower equivalent impedance (due to variations in manufacturing or temperature or whatever) will draw more current. This one will heat up
more, dropping in impedance even
more, and this unlucky LED will soon end up consuming
most of the power while the others consume hardly any.
He pops, and the next one follows. Give it a short while and they're all dead.
In a lower-power scenario, he might not pop, but he'll glow much more brightly than the others and the whole thing will look like crap.
If each one has a resistor, then if it starts to draw more current, its resistor will drop the voltage, providing a negative feedback effect which limits the current to a reasonable level:

The voltage drop across a resistor is
V which is equal to
I, the current through it, times
R, its resistance.
V=
IR, the definition of resistance. So, given a total 5V, and a 3.2V forward voltage, the resistor should have the remainder (5V - 3.2V = 1.8V) across it, with 24mA through it, so 1.8V/24mA = 75 ohms.
However - any LED drawing 24mA at 3.2V will be bright as fuck. Are you sure you want to run 24mA through them? Is this the desired current, or just the devices' maximum?