What kind of relay do I need for for 12V source with a 5V control voltage
In the comments, efox29 found a datasheet for this relay which will help in my answer. (Thanks!)



There are two parts of a relay to look at:



Coil

Your control voltage needs to match the coil voltage. They're both 5 V here. Good.

Your control output needs to supply enough current to make the coil work. The datasheet says that this relay takes 71.4 mA of coil current. That's quite a bit, and it's definitely more than an Arduino can source. I don't know what you're planning here - you should look at driving the coil with some sort of transistor driver.



Load

The relay needs to be able to withstand the load voltage when it's off. Here, the contacts are rated to 30 VDC, and the highest voltage in your system is 12 V. Good.

The relay needs to be able to pass all of the current into your load. The link says 10 A. You didn't say anything, so I can't confirm this. If your solenoid's required current is less than 10 A, this is fine.