Does Scrum support a 3 to 5 business plan?
I'm new to Scrum. In my business experience, we have always developed a 3 to 5 year business plan. Is this something Scrum supports?
Yes, to the extent that such planning is informed through empirical evidence.
...informed through empirical evidence.
As @Ian says, if you make a plan and do not expect it to be changed based on what you learn then stick with waterfall. But if it is widely understood and accepted that you will be constantly learning new things, adjusting based on what you learn, and that the plans will most likely change often then you should be able to use Scrum.
My experience and some circumstantial evidence for you. I've worked where 3 year plans were made and we did Scrum. I worked there for 5 years. The 3 year plan was adjusted on a quarterly basis and turned into a rolling 3 year plan instead of a fixed one.