yes there are many electromagnetic relays having the coil built for 5 Vdc and contacts suporting higher voltages and a few amps .
Not all relays are used for the same task and different relays can have different clamp voltages .
Usually they are built with coils for 5 , 12, 24 V in dc and 220, 380 V in ac . Rallays have several normally closed and/or normally open contacts
You can use electromagnetic relays to command power circuits, to multiply contacts or to detect treshold voltages.
Advantages : the command circuit (as your PIC mcu) is electrically separated from the power circuit (as your pump).
Disadvantages : they take a little power from the command circuit (you feel that when you are runing from baterys), contacts get used after a time
About using them as contact multiplyers: Suppose you have a number of consumers powered from diferent electrical circuits (ac power line, battery's, ....) , and want to start and stop them with a single button, you can use an electromagnetic relay that has sufficient contacts for each of your consumer.
Using electromagnetic rellay's for detecting treshold voltages: for exemple if you put a 12 V rellay in a circuit, when the voltage in the circuit is below ~7V the rellay will not clamp. Abowe ~7v the rellay will clamp and it's normally closed contacts will open and it's normally open contacts will close