NEVER use a program that claims to make things faster, try calling Apple support and see if they can help you over the phone 0800-692-7753

It's most likely your hard drive that needs replacing.

I'd suggest taking all the files/documents you want to keep, completely wipe the iMac, and start from scratch.

Make a backup in case it all goes horribly wrong, but don't use this backup to restore from as it will keep whatever crap software is potentially slowing it down.

How much RAM does the machine have? As lNomNoml said, it may be your hard drive beginning to fail. You can use Disk Utility to check for any errors if this is the case.

Is it the entire machine which is slow, or only certain applications?

Don't bother with any software which claims to speed up machines, they can cause more problems than they solve.

Is it a fusion drive? If it is consider getting it upgraded to an SSD.

I'd factory reset first then if that doesn't help look at RAM and SSD upgrades.

Handle9:

Is it a fusion drive? If it is consider getting it upgraded to an SSD.

I'd factory reset first then if that doesn't help look at RAM and SSD upgrades.

I highly recommend the following: (no screaming from the pews please)

I have been using this program for years, it is what I call a "Grease & Oil Change" maintenance program called Onyx. This is a FREE program that is a multifunction utility that you can use to verify the structure of the system files, to run miscellaneous maintenance and cleaning tasks, to configure parameters in the Finder, Dock, Safari, and some of Apple's applications, to delete caches, to remove certain problematic folders and files, to rebuild various databases and indexes, and more. I always use it prior and post system OS updates and about once a month. Also especially in this case concerning the new macOS 10.15.* Catalina which has dropped support for ALL 32 bit App's.

This program is available here: Titanium Software - Onyx ONLY DOWNLOAD THE VERSION FOR YOUR macOS

It is free from ALL malware, viruses & ransomware.

In the maintenance Tab I tick everything and in Options I tick everything except Bookmark icons & Form values.

I use this program prior to and post most iMac OS updates or when I have been doing some very heavy lifting like photo or movie work.

I also use another free wee program to uninstall programs instead of relying on the "move to trash to uninstall": I achieve this by using a FREE program called AppCleaner which you can download from here. Just drag the app you no longer want over this app. On using this App place a check mark IN ALL the boxes. It picks up all the program cache's which tend to be left behind.

Handle9:

 

Is it a fusion drive? If it is consider getting it upgraded to an SSD.

 

The base iMac, even today only have a 5400rpm drive, not even fusion. Apparently that finally goes away at this WWDC. If that's the case, then SSD will be your best path for sure. 

As for cleanup tools, as above has put OnyX is about the only tool i would trust on a Mac. 

Thanks all for your helpful comments. I have run the Onyx clean up and that has helped quite a lot. I think a hard drive upgrade will be needed in a while.

Regards

Clive