What is the best way to convert a 10V power supply into a 5V power supply?
If you want to convert the voltage to 5 volts, you should not use a resistance-voltage divider. That way you will indeed create 5 volts, but as soon as you apply a load the voltage will drop.
Instead, you have two options in general to regulate voltage. The first option using a linear regulator, and the second option is using a switch-mode power supply.
Linear Regulator
A linear regulator like for example the LM317 is a simple device that will act like a constantly adjusting resistor to lose the superfluous voltage (in your case 5v). The main advantage of using a linear regulator is that provides a nice and clean voltage source, without ripple. This is useful if the device your are powering requires no noise. Another advantage is that linear regulators usually are cheap, and easy to get.
The main disadvantage of a linear regulator is that it dissipates the superfluous voltage as heat. This way it is not efficient at all. In your example that translates to roughly 50% efficiency, since you only use 50% of the voltage.
Switch-mode power supply
A switch-mode power supply uses somewhat more advanced circuitry to only draw as much current as it needs in the input to then convert that energy to the required voltage. In your case, you would want to use a buck-converter, where it will take 10V at a 50% duty cycle to create 5V.
The main advantage of a SMPS is that it is rather efficient, and thus will not generate a lot of heat. The disadvantage is that they generate the required voltage based on a switching principle with frequencies varying from a couple kilohertz to a few megahertz, which introduces some ripple on your output voltage. This ripple is often expressed as a percentage of the output voltage.