external monitor 2009 imac

I have a late 2009 27inch imac (2560x1440 resolution) and i recently bought an external 28" 4k monitor, but it only gives me up to 1080p resolution -- I am using a minidisplayport to hdmi cable. In the Mac specs it says it allows up to full native resolution "Simultaneously supports full native resolution on the built-in display and up to a 30-inch display (2560 by 1600 pixels) on an external display" per Apple. I understand that I wont have 4k, but I should be able to get at least the same resolution as my imac screen right? Any ideas? (I've tried downloading switchresX, but no luck)