What is the max resolution of HDMI/usbC port can support A515-57T-77EC

Your Intel® Core™ i7-1255U GPU specs are as follows:

·      Intel® Iris® Xe Graphics eligible

·      Graphics Max Dynamic Frequency - 1.25 GHz

·      Graphics Output - eDP 1.4b, DP 1.4a, HDMI 2.1

·      Execution Units – 96

·      Max Resolution (HDMI) - 4096 x 2304 @ 60Hz

·      Max Resolution (DP) - 7680 x 4320 @ 60Hz

·      Max Resolution (eDP) - Integrated Flat Panel)‡ - 4096 x 2304 @ 120Hz

·      DirectX* Support - 12.1

The above processor gpu specs are the max specs what the graphics of your cpu can output as your preferred "hoping to get 2560x1440Hz with a 4k/60hz HDMI cable to my Asus MX27AQ monitor" should not be a problem but use the HDMI 2.1 cable as every resolution upside has compromises of a downside especially with integrated graphics. I've got a Acer Nitro 5 15.6-inch i7-11370H/8GB/512GB SSD/GTX1650 4GB Gaming Laptop that I’m using with an external 27” 165Hz/1ms monitor with the Intel® Iris® Xe Graphics also and it works fine, I also run its settings at default 1920x1080 resolution / 144p but, this laptops secondary GTX-1650 gpu I've changed its settings in the NVIDIA Control Panel to run software’s of games/editing with the GTX-1650 gpu only and its performing very well on both with the integrated i7 CPU/GPU and the GTX-1650 GPU.

Btw, the external monitor I'm using is the “ Dell S2722DGM 165Hz 1ms QHD Curved Gaming” and I use this monitor at 1920x1080 resolution / 144p also, I have tried to up to resolutions of and like you want to "2560x1440Hz / 60p and even above and it also worked on both gpu’s very well but, this works at a compromise of the image and fps, as all these gpu’s can run 4k monitors if you want, just don’t expect frame rates in games to keep up with things and temps to be normal as its a laptop and NOT a desktop. To be clear, older and budget GTX-1080 to GTX 1650 etc graphics card you can buy today will support output resolutions of 1440p or higher, but you won't necessarily be able to game at that resolution at a higher rates.

Btw, I’m using that above Dell monitor for gaming on a self-built AMD gaming rig of 5950Xcpu / ASUS TUF GAMING B550-PLUS (WI-FI) / Antec Torque TG wid-tower case / MSI GeForce RTX 3080 Ti Gaming X Trio 12GB / 64GB (2x 32GB DDR4-3600 CL18) / Corsair HX1000W psu etc etc and it works at those higher resolutions very well without any fps drops and no problems and clear as a whistle performance, so remember all the above are the compromises that you have to make to whatever suits you? Good luck and hope this helps you out