Kodak ESP5250 - a quick search of the Kodak downloads seems to only produce a driver pack dated 22nd October 2015, and that says that it is compatible with MacOS versions up to 10.11.x. So the answer appears to be probably not.
Unfortunately manufacturers aren't very good at keeping old products up to date for new system versions. That may be to do with the fact that they make their money from selling you new devices, although some manufacturers are better than others.
In addition in this case, given that Kodak exited the inkjet market altogether back in 2012 or so, and this device dates back to 2010, I am afraid that the time has almost certainly come to move on to a different manufacturer and a new printer.