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Look at the small letter/number combination on the back of your stock wheels. That is the offset. Might be ET17 or something like that (less than EF20) for an E39 530i. You probably installed wheels not meant for the E39 that have much more offset, like ET40, moving the wheels nearly an inch inwards. The good news is that spacers will move the wheel out. ET40 with a 20mm spacer is like an ET20, which may be closer to what you want.
The next problem is tire aspect ratio. As you increase the wheel diameter you need to decrease the adjective ratio, assuming the same tire width (aspect ratio is percentage of tire width), in order to maintain the same overall tire circumference so the tire and wheel combination fit properly. For 18” tires you probably want to a 40 series rather than a 55 series, but since aspect ratio is related to width, you could alternatively run skinnier tires than stock and maybe end up with something workable. Too wide can also lead to problems, but you did not specify the width that is causing problems.
The good news is that google can help you figure this out. Google 18” wheels and tire sizes for BMW E39 and start reading and learning.
Beware also that the E39 has a funny hub size and some wheels not made for the E39 require hub bore adapters. I don’t like them and recommend buying wheels that fit without adapters. Spacers are fine, but if adapters were required I would look at different wheels.
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