OP:
There's a combination of three things slowing down the iMac.
1. internal platter-based hard drive
2. new version of the OS
3. older Mac.
The unspoken reality about Apple's newer OS releases is that they require either an SSD or a fusion drive (which is "part SSD") to run at acceptable speeds.
Having both an older Mac -and- a platter-based hard drive inside is killing the speed. The OS is "running" (technically), but from the viewpoint of the user, it's more like "walking".
Reply 2 above has "the answer" to make it run faster.
That is, you need to get an external thunderbolt-based SSD, and set that up to become your "external boot drive". If you do this, things will go MUCH faster.
The downside is that thunderbolt is expensive (compared to an external USB3 SSD drive), but since you don't have USB3, it's really the only choice UNLESS you were to pry open the iMac and put a SATA-based SSD inside it.
If you intend to keep the iMac a while longer (say at least 2 years), I'd go the external thunderbolt SSD route.
I'd get a smaller-sized SSD (256gb) -- cheaper.
I'd put the OS, applications, and basic accounts on the SSD (keep it "lean and clean").
I'd leave the large libraries of music, movies and pictures on the internal HDD (they don't need the speed)
Your other alternative is to start shopping for something new or perhaps Apple-refurbished.
IMPORTANT -- do not, repeat DO NOT buy another iMac with a platter-based HDD inside.
Buy ONLY one with an SSD or a 2tb fusion drive (I'd avoid the 1tb fusion drive as the SSD portion is only 32gb).
"Straight SSD" is the way to go on the new ones...