IP Default-Network

[Fuzz]

network 10.10.0.1 0.0.0.0
network 10.10.5.5 0.0.0.0
network 10.0.0.0

The last network command here makes the first two obsolete. This command tells every interface beginning with 10. to be a part of EIGRP. You are not telling EIGRP to advertise the 10.0.0.0/8 network.

Try this:

Remove anything with 10.0.0.0 in the configuration. Set 10.0.16.1/21 as a loopback interface. Now add 10.0.16.1 into EIGRP. Now issue the command ip default-network 10.0.16.0.

At the moment, your hub router thinks that network 10.0.0.0 has a route for any network not in it's own routing table. To reach network 10.0.0.0, it has to send packets to 10.0.16.0, which is a null route. You need to make this router believe it has the default route, and that other routers should use 10.0.16.0 as a default route. It has to be advertised by EIGRP so that every router knows how to reach the 10.0.16.0 network.