We report an improved geo-neutrino measurement with Borexino from 2056 days of data taking. The present exposure is $(5.5pm0.3)times10^{31}$ proton$times$yr. Assuming a chondritic Th/U mass ratio of 3.9, we obtain $23.7 ^{+6.5}_{-5.7} (stat) ^{+0.9}_
{-0.6} (sys)$ geo-neutrino events. The null observation of geo-neutrinos with Borexino alone has a probability of $3.6 times 10^{-9}$ (5.9$sigma$). A geo-neutrino signal from the mantle is obtained at 98% C.L. The radiogenic heat production for U and Th from the present best-fit result is restricted to the range 23-36 TW, taking into account the uncertainty on the distribution of heat producing elements inside the Earth.
