Cisco router cannot ping subnet

Hosts from subnet 192.168.65.0/24 has correct default gateway IP address configured?

Logic:
Traffic from router is sent from closes interface.
When ping is sent from router it is sent from the interface that belongs to the same subnet.
When you are pinging neighboring router ping is sent from directly connected interface.

Since there are only two directly connected routers involved and router in the middle can reach both networks, most likely, issue is device that received ping has  no idea where to return traffic.
That is if I correctly understood issue.

Is the 10.5.5.1 address the only interface on router 2?  When you ping 192.168.65.0 are you pinging the inside interface of R1?  If R2 has more than one ip'd interface, you may need to ping and specify the source you are pinging from.

Also, topology and configurations are helpful. :)

@Justincase - As I thought about it more and more, that is what I was wondering. I am in the process of adding a PC and a switch to the 10.5.5.2 router (port 2 and different subnet).

@soulja - this maybe the root of the issue. Router 1 fa0/0 - 10.5.5.1 -- fa 0/1 192.168.65.16 (plugs into our network so that I can remote into from my laptop). Router 2 fa 0/0 - 10.5.5.2 -- fa 0/1 10.5.4.0/24. Router 2 fa0/2 will be plugged into a switch then into a PC.

My apologizes if that is confusing.

So you need to make sure you choose the source of your ping and that the alternative router has a route back to the source of the ping. Until you get hosts setup you can just ping the router interface that is the gateway to the hosts. In this case for example you would ping from router 2 with a source of fa0/0 and ping R1's fa0/1 interface ip.