Without doubt the issue here is with the Hard Drive which is more than likely 5400rpm. I thoroughly recommend upgrading to a Hybrid Drive and performance will increase dramatically I have done the same with one of my iMacs which is the identical model
https://www.seagate.com/gb/en/solutions/solid-state-hybrid/
https://www.ifixit.com/Guide/iMac+Intel+21.5-Inch+EMC+2889+Display+Replacement/57815
Hey Guy hard to find out what the RPM's are but I believe you are correct that mine is 5400. Where you able to address the lack of RAM in anyway?