I have to convert to .DNG with an Adobe external tool before use in Photoshop because Photoshop doesn't recognize the Raw file that my Nikon D5000 produce. Is that normal that I have to convert all pictures before processing them in Photoshop?
You should probably update your Photoshop or Adobe Camera Raw (not sure it can be updated separately) to ACR version 5.4 or later, because D5000 was not supported in the previous versions of ACR.
Photoshop has a Camera Raw plug-in. You just need to update it to the most recent version.