To add a temporary route:
ip route add 172.16.5.0/24 via 10.0.0.101 dev eth0
To make it persist system or network settings restart, create a route-ifname file for an interface through which the subnet is accessed, in this case eth0:
nano /etc/sysconfig/network-scripts/route-eth0
Add the line with the network settings for the other subnet:
172.16.5.0/24 via 10.0.0.101 dev eth0
If your computer is on a network and is not directly connected to the internet, it will be configured with what is called a default gateway, which is usually a router. If the computer cannot find the specific IP address on its local network (aka broadcast domain), as defined by its subnet, it will forward any packets headed to that IP address to the default gateway. The gateway will then attempt to forward packets elsewhere, such as the internet, or another broadcast domain