If I use a 70-300mm VR which is a FX lens on my DX format D90. The FX focal format is about 1.5 X larger than the DX format. The result is that on my D90 I have in effect a 105-450mm lens.
There is no reason whatsoever. You gain access to a lot of nice glass and when Nikon stops making DX cameras and lenses, you have lenses that can be used on nearly any Nikon 35mm camera, since the F.
Yes, there definitely could be... If the FX lens is not designated AF-S or AF-I (such as only AF or AF-D or AF-G), you definitely will not be able to autofocus with it on your D5000 and will have to use only manual focus instead. Because your D5000 is not only a DX type, it also doesn't have an AF motor inside it and requires lenses that do (AF-S, AF-I)....
Using an FX lens on an FX camera is where you get the complete true focal length image on the sensor and card.
However If you use it on a DX camera you will get a cropped image that also appears to be telephoto enlarged 1.5X, just exactly the same way a DX lens works on a DX camera!
So if you use an FX style f1.8 50mm lens on a DX camera you will actually be getting a magnified focal length of 1.5x, which = 75mm. And likewise an FX 85mm on a DX camera will give you128mm, and a 105mm will give you 158mm!