2013 Macbook Air not showing 1440p Option on External Display

I have a mid 2013 Macbook Air with the Intel HD 5000 graphics chip. I recently purchased a 27" Acer K272HULbmiidp 1440p (2560x1440) monitor that just arrived today. I connected it via a mini displayport to HDMI cable, and was immediately greeted with awful graphics that didn't fit. Turns out its a common issue with external displays on macs, which assume settings for a TV not a monitor. Basically, I fixed it by using a Ruby script to force RGB mode onto the monitor. So that's all good now.

The issue is I can't seem to get the 2560x1440 option on the external display, it will only show 1920x1080. I have heard the mini displayport to display port cable will allow my computer to run an external monitor in 1440p. Is this true? Please suggest what I can do to get the external display running in 1440p. Thank you so much guys.

Did you check if you have a Display Port on the monitor apart the HDMI? I had the same issue with my late 2012 mac mini, and I had to buy a mini DisplayPort to DisplayPort to use the 1440p resolution