What Arduino board are you using? For instance on a Nano, stick to something like 200mA absolute maximum on 5V and <5mA max on 3.3V (since 3.3V is made by the CH340 which is NOT a power supply).
Please keep in mind the PMS5003 wants to be fed with 5V, but should be interfaced with at 3.3V. So if you use something like a Nano, UNO etc or another 5V board be sure to use logic level converters between the Arduino and the PMS.
How would a relay help in this? A relay is simply a switch - it switches something on or off. It does nothing to change the matching of a power source to the demands of a module. If you want to supply something with power, even for a short period of time, the power supply needs to be up to it.
I don't think you need a relay here as it seems the PMS5003 can be put to sleep simply by pulling pin 3 low. No relay needed or anything.