Step up 3.3V to 5V and draw 500mA without a voltage collapse/break down
a generic answer:
Your module has to be able to provide at least 500mA - however usually in engineering you have to account for certain safety margin - so if you need exactly 500mA output, the module should be able to provide more (how much is a different topic then your question, but still important to consider in your design).
So as a ballpark calculation Id calculate like this:
With Safety factor i: 1.5
P_out = I_out  * U_out * i = 0.5A * 5V * 1.5 = 3.75W
As you boost converter has only a certain efficiency the input power into it should be higher:
With a efficiency n_eff of 85% &lt;- just a generic value as example, you should check the data of your module
P_in = P_Out / n_eff = 3.75W / 85% = 4.41W
Out of this input per you can calculate what supply is necessary for the module:
I_in = P_in / U_in = 4.41W / 3.3V = 1.34A
So if your 3.3V power supply can provide 1.34A and your module 0.75A / 3.75W, then you should not see the voltage stop with a static 10Ohm load resistor.