How can I be sure to supply enough current without increasing the voltage?
No you cannot, according to Ohms law, which we think is pretty well solid (It's a law, not a theory!).

As long as your 5V source can output the required current while maintaining it's regulated voltage, you are okay. 

if the 5V source is weak, and cannot output enough current for the load, then the output voltage will go out of regulation and will drop. This is evident with short circuits, where the load is essentially approaching 0 Ohms, which is effectively requesting infinite current from the voltage source. The voltage source is non-ideal though, and has inherent resistance either from the energy source itself, or other physical entities like resistance in the wire etc. A short circuit will see the output voltage drop to almost 0V, with extremely high current, until something explodes. Obviously a weak powersupply will just sit there at ~0V output until the short is removed - however usually they will fail in this condition after a prolonged time.

The important thing here is engineering a solution which allows for a power source which can support all the connected devices. If you need 0.5A of total output current, then play it safe and get a 1.0A capable power supply for the voltage you need. If the power supply is slightly overrated then it can handle extended large current spikes from the loads without causing brownouts or other issues with a sagging voltage supply. 

Another common technique called Power Supply Decoupling or Bypassing is to use Capacitors as miniature current reservoirs, which can support the power supply's output by providing the short bursts of current which a load needs before the power supply even sees the change in demand. If a power supply has poor line/load regulation specs, usually coming from a poor transient response to load changes, its output voltage may sag significantly before it can recover if the loads are heavy duty and fast-changing, and if there is not enough output capacitance. 

One more comment about "making more current" flow into the loads - the loads will only consume as much current as they need. You cannot push more current into something unless you increase the voltage, which is silly in this case. The Load may decrease it's internal resistance, thus consuming more current at the fixed voltage it expects. The key point here is you cannot squeeze more current into the same sized hole, but make sure you have enough output current available for your power supply so that if the hole suddenly (or even over a long time) changes it's need for current, you can provide it without loss of regulation. 

In summary, choose the appropriate voltage supply which can deal with the load's expected average current draw, usually with a current output safety factor of 1.3 -> 1.5 or more. Then you must ensure there is enough capacitors involved to handle fast changes in the load, to avoid noise, brownouts, and other issues which occur due to insufficient power supply decoupling.