The Galactic bulge is dominated by an old, metal rich stellar population. The possible presence and the amount of a young (a few Gyr old) minor component is one of the major issues debated in the literature. Recently, the bulge stellar system Terzan 5 was found to harbor three sub-populations with iron content varying by more than one order of magnitude (from 0.2 up to 2 times the solar value), with chemical abundance patterns strikingly similar to those observed in bulge field stars. Here we report on the detection of two distinct main sequence turn-off points in Terzan 5, providing the age of the two main stellar populations: 12 Gyr for the (dominant) sub-solar component and 4.5 Gyr for the component at super-solar metallicity. This discovery classifies Terzan 5 as a site in the Galactic bulge where multiple bursts of star formation occurred, thus suggesting a quite massive progenitor possibly resembling the giant clumps observed in star forming galaxies at high redshifts. This connection opens a new route of investigation into the formation process and evolution of spheroids and their stellar content.