Aims: The CoRoT space mission continues to photometrically monitor about 12 000 stars in its field-of-view for a series of target fields to search for transiting extrasolar planets ever since 2007. Deep transit signals can be detected quickly in the “alarm-mode” in parallel to the ongoing target field monitoring. CoRoT's first planets have been detected in this mode. Methods: The CoRoT raw lightcurves are filtered for orbital residuals, outliers, and low-frequency stellar signals. The phase folded lightcurve is used to fit the transit signal and derive the main planetary parameters. Radial velocity follow-up observations were initiated to secure the detection and to derive the planet mass. Results: We report the detection of CoRoT-5b, detected during observations of the LRa01 field, the first long-duration field in the galactic anti-center direction. CoRoT-5b is a “hot Jupiter-type” planet with a radius of 1.388+0.046-0.047 R_Jup, a mass of 0.467+0.047-0.024 M_Jup, and therefore, a mean density of 0.217+0.031-0.025 g cm-3. The planet orbits an F9V star of 14.0 mag in 4.0378962 ± 0.0000019 days at an orbital distance of 0.04947+0.00026-0.00029 AU. Observations made with SOPHIE spectrograph at the Observatoire de Haute Provence (07B.PNP.MOUT), France, and HARPS spectrograph at ESO La Silla Observatory (072.C-0488(E), 082.C-0312(A)), and partly based on observations made at the Anglo-Australian Telescope. The CoRoT space mission, launched on December 27, 2006, was developed and is operated by CNES, with the contribution of Austria, Belgium, Brasil, ESA, Germany, and Spain.