Camera don't make pictures, people with skills make pictures. D5000 is a fine camera, you just need to learn it inside out and learn more about photography. Yes, your kit lens can be limiting. Instead of shelling out 3K, why not buy better lens and try your luck. Try a 50mm prime lens (the one with the motor built in, since d5000 does not) for family portrait and night photography,85mm for headshots. If you're not happy with the quality of your kit lens for landscape, try tamron 17-50mm or if you want to go wider, try tokina 11-16mm. Becareful with wide angle lens for perception, distortion and closenes to the subject. Try a telephoto lens to zoom in subject closer, like 70-300mm. Experiment with different lens and feel the differences. Educate yourself about composition, lighting, creativity and post processing, those will take you a long way. Look at other people's work and try to find out how it is done, try to copy it, you'll learn a lot. For portrait, there is a universe of knowledge to learn about speedlights, strobes,umbrella, soft box and many many more.
Don't assume buying the newest will give you better pictures. For years, I had the D5000 and I used it to the max, I learnt a lot from that single camera. Trust me, I did better than friends who had expensive ones. I'm happy I didn't follow the latest and greatess. Limiting yourself will make you think outside the box when you've mastered all the possibility.
My 2 cents. Happy shootings.