RAM Upgrade.

Yea' it looks like someone has mistakenly put the wrong and slower RAM into that iMac.

At this point I think your best bet, is to buy the OWC 16GB, 24GB or 32GB kit, that macjack and I have both recommended.

I recently retired the same model with 12GB RAM and, like Macjack, I never found it short of RAM. Most reports of slow 2010/2011 iMacs come down to a struggling hard drive or conflicting software.

Too often, users load up their Macs with useless third-party utilities like anti-virus and "cleaning/tune-up" apps that only degrade performance while giving absolutely no benefit. This Apple article is about determining if software is the problem and uses Apple software that came with you computer:

See how apps affect Mac performance, battery runtime, temperature, and fan activity - Apple Support

Two things to note:

1) Step 1 is critically important to getting any useful information from the test.

2) The display is dynamic so you need to watch it for at least 30 seconds to spot resource-grabbing tasks that could be suspects.

The dynamic display also makes screenshots posted here only minimally useful. Make a note of the the name of any process that is using a lot of resources and post it here. NOTE: it is nromal for the process "kernel_task" t use a lot of CPU cycles. That one is expected.

Double check to make sure that your iMac is not a Late 2009, which uses 1067MHz modules.

see > Find the model name and serial number of your Mac - Apple Support

and/or > Identify your iMac model - Apple Support

Because a Mid 2010 iMac is suppose to use and have 1333MHz modules installed in it.

see > https://eshop.macsales.com/shop/memory/iMac/2010/DDR3_21.5_27

and/or > https://support.apple.com/kb/SP588?locale=en_US

Here are the specs on mine. Yours is a core i5 which according to specs also takes 1333MHz.

Yours:

https://everymac.com/systems/apple/imac/specs/imac-core-i5-2.8-27-inch-aluminum-mid-2010-specs.html

I would replace all RAM with 1333 MHz modules. But you can double check this with OWC and Crucial by using the tool on their sites or call and ask.

I have the same model iMac with 12 GB and it runs well for my needs. I rarely find myself using any swap. Depending on which apps you run you may or may not need to upgrade the RAM. Take a look in Activity Monitor > Memory and check the graph at the bottom. If it is running in the red zone, that would indicate that you need more RAM.

If you do need RAM, know that Macs are fussy about RAM.  Both Crucial and OWC are reliable vendors with high quality RAM. You can find the RAM modules that are right for your Mac by using the tool on either site. (Mine are 1333 MHz DDR3 )

If it is running slow and RAM isn't the issue, I'd suggest upgrading the hard drive to SSD. This will make a dramatic improvement. You can find those on OWC, a good source for all things Mac.