Carbonaceous chondrites are often considered potential contributors of water and other volatiles to terrestrial planets as most of them contain significant amounts of hydrous mineral phases. As such, carbonaceous chondrites are candidate building blocks for Earth, and elucidating their thermal histories is of direct importance for understanding the volatile element history of Earth and the terrestrial planets. A significant fraction of CM type carbonaceous chondrites are thermally metamorphosed or "heated" and have lost part of their water content. The origin and the timing of such heating events are still debated, as they could have occurred either in the first Myrs of the Solar System via short-lived radioactive heating, or later by impact induced heating and/or solar radiation. Since Rb is more volatile than Sr, and some heated CM chondrites are highly depleted in Rb, a dating system based on the radioactive decay of Rb-87 to( 87)Sr(lambda(87) Rb = 1.393 x 10(-11) yr(-1)) could be used to date the heating event relating to the fractionation of Rb and Sr. Here, we have leveraged the Rb-87/Sr-87 system to date the heating of five CM chondrites (PCA 02012, PCA 02010, PCA 91008, QUE 93005 and MIL 07675). We find that the heating events of all five meteorites occurred at least 3 Ga after the formation of the Solar System. Such timing excludes short-lived radioactive heating as the origin of thermal metamorphism in these meteorites, and relates such heating events to ages of collisional families of C-type asteroids.