Unable to get Arduino Ethernet Shield IP address connected to Raspberry
192.168.10.0 is not a valid IP address (unless it's on a /32 subnet which makes no sense on ethernet).  

You need to allocate a proper IP address within a proper subnet, such as 192.168.10.1/24 (i.e., IP 192.168.10.1 and netmask 255.255.255.0), and either manually provide a similar IP address to the Arduino (such as 192.168.10.2/24 [IP 192.168.10.2 netmask 255.255.255.0]), or install and configure a DHCP server on the Raspberry to hand out IP addresses within that subnet range (e.g., 192.168.10.100/24 to 192.168.10.200/24) for the Arduino to then be able to use DHCP mode.

Most of that is outside the scope of an Arduino SE site, though.