Absolutely! ; Any DSLR is a fine choice - they don't really make them bad nowadays. ; The D5000 is plenty capable, and you've got a good 'superzoom' type lens to get you used to the camera. ; Once you've got a hang of it, you'll probably want to start looking to add a low light prime lens or two, and once you figure out the focal ranges you most often use, you can look into picking up a nice lens with a shorter focal range to use when you only need that particular range - faster and better glass, less range.
Personally, I think a DSLR and a good wide-to-tele zoom is a nice way to start out with a DSLR and find out what types of shots you enjoy taking - then pick the lenses you would use most next. ; Congrats!