Slowdowns are almost always due to some malware or other misbehaving third party program. I doubt Sierra is the cause, as Apple is pretty good at supporting older hardware. Your best bet is to take your machine to the Apple store and ask the techs there to reinstall the Operating System (it's free). You are sure to see a big improvement in performance. However, you will have to reinstall all your apps. Make sure you backup your files before taking it there!