Yes a gpu running PCI 5.0 is backwards compatible with a PCI 4.0 slot.
Yes, but. As in yes, but you may not get top speeds from it. Probably not an issue in this case though.
Generally, PCIe auto negotiates transfer speeds and lanes. Similar to a USB drive. It will probably work, but will be limited to the lowest common transfer speed.
then i think i will probably pay more bucks for a pcie 5 motherboard
I don’t know what you are using the card for, but I don’t think you will be able to saturate that pcie5 speeds. In gaming and everyday usage at least you won’t be able to spot the difference.
Especially because the 9070 XT is slower and has less memory than the 7900 XTX - which is completely fine with PCIe 4.0. Bandwidth can only limit, not speed up, and to my knowledge there isn’t a card that would actually be limited by 4.0.