We describe the results from a new instrument which combines Lucky Imaging and adaptive optics (AO) to give the first routine direct diffraction-limited imaging in the visible on a 5 m telescope. With fast image selection and alignment behind the Palomar AO system we obtained Strehl ratios of 5%-20% at 700 nm in a typical range of seeing conditions, with a median Strehl of approximately 12% when 10% of the input frames are selected. At wavelengths around 700 nm the system gave diffraction- limited 35 mas full width at half-maxima (FWHMs). At 950 nm the output Strehl ratio was as high as 36% and at 500 nm the FWHM resolution was as small as 42 mas, with a low Strehl ratio but with resolution improved by a factor of similar to 20 compared to the prevailing seeing. To obtain wider fields we also used multiple Lucky Imaging guide stars in a configuration similar to a ground layer AO system. With eight guide stars but very undersampled datawe obtained 300 mas resolution across a 30'' x 30'' field of view in the i' band.