The base five system uses groups of five just like our base ten system uses groups of ten. The possible digits in the base five system are 0, 1, 2, 3, and 4, so the face values are 0-4. The place values are powers of five. Every time we reach five units we call them a group and rollover a place value. When we reach five groups of five we regroup and rollover another place value.
Counting in base five can be modeled by counting with only one hand instead of both hands, like we do in base ten. We can also use the idea of money, with pennies, nickels and quarters. This number system can also be modeled using base five blocks.