They are equilibrium points between gravity of the two bodies and the fictitious centrifugal force. Three are on the line between the two bodies (one one each s

They are equilibrium points between gravity of the two bodies and the fictitious centrifugal force. Three are on the line between the two bodies (one one each side and one in the middle) where these forces cancel. The other two are also points where these cancel, on the sides, but the cancelation is component wise since the forces aren't all collinear at these point. Two because one on each side.