Upgrade From Leopard to...

Do you have a local friend with a Mac that does support Mavericks? Use their Mac as a "mule" to download the OS and build an install drive, then you can use that to wipe your Mac (I don't believe you'll be able to do an in-place upgrade) and install Mavericks clean. You'll need to back up your data. Unfortunately, the only OS available on the Mac App Store is Sierra so that friend needs to have downloaded it before. This all assumes your Mac is actually on the support list for Mavericks.

 

You can purchase the Snow Leopard disk from Apple:
https://www.apple.com/shop/product/MC573Z/A/mac-os-x-106-snow-leopard

Apple no longer has the Mavericks download available unless you had previously "purchased" (downloaded) it. Your choices for Mavericks are:
Get it from a Mac friend that had previously downloaded it and make a USB installer.
Buy a Mavericks USB installer from Amazon or eBay.

EDIT:
Since the highest OS your iMac supports is El Capitan and not Sierra, Apple does provide a way to get 10.11.6:
https://support.apple.com/en-us/HT206886

 

I suggest that your best options would be to go to either:
1. 10.6.8 Snow Leopard (installer DVD available from Apple)
or
2. 10.8.5 Mountain Lion (get USB flashdrive from ebay with copy of ML installer on it)
or
3. 10.11.6 El Capitan (get USB flashdrive from ebay with copy of El Cap installer on it)

BE AWARE that with the advent of 10.9 (Mavericks), Apple seems to have re-worked the OS to run its best on Macs that have either SSD's or "fusion drives" in them. Not so much for older Macs with platter-based hard drives.
I realize that "the perception of speed" is a personal issue, and that what I find to be "slow", you may not.