Results of photometric surveys have brought to light the existence of a population of giant planets orbiting their host stars even closer than the hot Jupiters (HJ), with orbital periods below 3 days. The reason why radial velocity surveys were not able to detect these very-hot Jupiters (VHJ) is under discussion. A possible explanation is that these close-in planets are short-lived, being evaporated on short time-scales due to UV flux of their host stars. In this case, stars hosting transiting VHJ planets would be systematically younger than those in the radial velocity sample. We have used the UVES spectrograph (VLT-UT2 telescope) to obtain high resolution spectra of 5 faint stars hosting transiting planets, namely, OGLE-TR-10, 56, 111, 113 and TrES-1. Previously obtained CORALIE spectra of HD189733, and published data on the other transiting planet-hosts were also used. The immediate objective is to estimate ages via Li abundances, using the Ca II activity-age relation, and from the analysis of the stellar rotational velocity. For the stars for which we have spectra, Li abundances were computed as in Israelian et al. (2004, A&A, 414, 601) using the stellar parameters derived in Santos et al. (2006, A&A, 450, 825). The chromospheric activity index S_US was built as the ratio of the flux within the core of the Ca II H & K lines and the flux in two nearby continuum regions. The index S_US was calibrated to Mount Wilson index S_MW allowing the computation of the Ca II H & K corrected for the photospheric contribution. These values were then used to derive the ages by means of the Henry et al. (1996) activity-age relation. Bearing in mind the limitations of the ages derived by Li abundances, chromospheric activity, and stellar rotational velocities, none of the stars studied in this paper seem to be younger than 0.5 Gyr.