This could be due two things see @admon reaction, but also it can be dhcps rebind protection.
Does pinging to the wireguard virtual ip work?
edit:
I also notice this:
10.0.0.5/24 usually this is not recommended for a site to site vpn, you essentially want:
the server needs:
10.0.0.1/24 <- many people including myself make the mistake in turning this into a host bit, if it looks like that ending with 0/24 that is wrong this can also be a cause it is not working.
For the peers its better to use more abstract approach:
You use 10.0.0.5/32 and for allowed ip: 0.0.0.0/0 on the client.