Hi. Recently i have bought new pc, with intel i5-11500 and their integrated graphics card. It works properly on windows but i have a problem with drivers on linux - it does not depend on distribution, i have checked both on fedora and ubuntu(mint). I have been trying to resolve this problem on my own but i have no more ideas. So basically I have no choice on resolution - the default and unchangeable is 1024x768. I tried to add something in grub options just as i saw in the internet but maybe I do it wrong? Please give me some help, cuz its really annoying working on such resulution.
https://paste.pics/70b9e75217b1c334a714c1e19fe00624

Without mentioning distro versions tried, you haven't told us much. You have Intel Rocket Lake, which because rather new, needs recent kernel. You probably should be OK if you're trying openSUSE Tumbleweed, Fedora 35, Ubuntu 21.10 or other very recently released (or about to be released) distros with a current kernel version, e.g. 5.14.9. Diagnosis relies on you providing data. One data point would be solved by uploading Xorg.0.log. This should be found in /var/log/Xorg.0.log or ~/.local/share/xorg/Xorg.0.log. So on Fedora, do cat /var/log/Xorg.0.log | fpaste or cat ~/.local/share/xorg/Xorg.0.log, according to whichever location you find this file. On Ubuntu, substitute pastebinit for fpaste, and for openSUSE, substitute susepaste. Also paste here output from inxi -SGa using code tags around your paste.

FWIW: any of the newer (non-LTS) Ubuntu work with RKL (21.10 is not the only option). Agree with the rest - we need to know specifically what was tried before saying 'well it can't work' - my guess is that a very old version was tried, and there's no driver support there.