Agree with the DDR5 tip, its definitely worth it now. If you're watching every penny, the Gigabyte B760M DS3H AX DDR5 is usually a bit cheaper than the MSI. Its got two PCIe 4.0 M.2 slots and decent enough power delivery for a locked i5. Just keep in mind it uses a slightly older audio codec, but for gaming you probably wont even notice the difference honestly.

Basically, if you are building fresh today, I'd strongly suggest going the DDR5 route. The performance jump is getting more noticeable and the price gap is tiny now. For a solid budget pick, check out the MSI PRO B760M-A WIFI DDR5. It has two M.2 slots and the VRM cooling is actually pretty decent for the price point. If you really want to save every penny, the Gigabyte B760M DS3H AX DDR5 is a classic value choice. I've used the DS3H in a couple of builds and it's super reliable. I personally prefer the MSI board because the layout is cleaner for cable management. Both have the wifi you need and wont hold that 13400 back at all. Ngl, the ASRock B760M Pro RS/WIFI is also a sleeper hit if you want something that looks a bit more premium without the extra tax.

I totally agree with going for a B760 board instead of a pricier chipset. For an i5-13400, anything more is just overkill and wont actually boost your performance in a noticeable way. I've looked at the technical data for several entry-level B760s lately and the power delivery is usually more than enough for that 65W TDP chip, even when it is boosting under load. One small point though... definitely check if the board has a heatsink on at least one of those M.2 slots. Some budget boards leave them bare, and those NVMe drives can get pretty toasty during long gaming sessions. Also, since you're choosing between memory types, I'd say go DDR5. The price parity is finally here and the bandwidth specs are just better for future-proofing. Good luck with the build!