It looks like this laptop has an optional [link|https://laptop.bg/system/images/221841/original/ROG_Stryx_G531.png|USB Type-C port on the back], between the HDMI port and DC barrel plug. If equipped, that Type-C port is capable of native DisplayPort output, which would actually be superior to HDMI in terms of resolution + refresh rate. You would need a simple [link|https://www.cablematters.com/pc-1038-125-usb-c-to-displayport-adapter-8k-ready.aspx|USB Type-C to DisplayPort adapter] if your monitor does not have a native USB Type-C input. If you prefer using HDMI (or if that is all your monitor supports), I am confident you can use a similar USB Type-C to HDMI (4K@60Hz) adapter with good results.[br]
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However, if your laptop is not equipped with that USB Type-C port, then I would agree that the trying to adapt the USB Type-A ports would be inadvisable since those ports are not wired for display output. You could look into eDP (embedded DisplayPort) to HDMI/DisplayPort converters if you don't need to use the laptop's internal display. That port does have the capability of outputting at the same resolution or greater than the original HDMI port, as long as the converter itself is capable of that. The HDMI port on the laptop is HDMI 2.0b, so look for [link|https://www.laptopscreen.com/English/section/Articles/?mode=5&view_article=1508175591|eDP (you'll have to figure out which kind your laptop has)] to HDMI 2.0b if you want a direct replacement. Make sure whatever converter you get is compatible with your laptop's panel, which you can find the model of using a tool like [link|https://www.nirsoft.net/utils/dump_edid.html|this]. Not all eDP is wired the same, so make sure that the converter is wired the same as your laptop. [br]
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In terms of replacing the HDMI connector itself, that would be extremely difficult and risky to perform, unless you have experience as you mentioned. My best advice, if you do have to go that route, is to spend a good chunk of time researching on YouTube and watching tutorials of people performing these repairs. Then, if you can, see if you can practice your soldering skills on something less valuable/easier to work on before attempting such a repair. [br]
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Hopefully these tips help, and best of luck with your repair endeavors!