OSPF traffic flow

Hi,
The answer is positive. Though the neighbor relationship between the R1 and R3 is down, the network between R1 and R2 will be received from the R5. And the network between R1 and R3 could be advertised to R2 through R1, network between R3 and R5 will be advertised to R2 and R1 through R4.
The conclusion is when R3 ping the network with source set as the IP address of interface which connect to R1, the ICMP flow path would be R3 > R5 > R4 > R2, and the reply path would be R2 > R1 > R3. When the ping packets source is set to address of interface which connects to R5, the ICMP echo and reply path are the same, R3 > R5 > R4 > R2.
What should be pointed out is that when the neighbor between the R1 and R3 is fine, the type 3 LSA describe the network between the R1 and R2 will not load into the OSPF routing table on R3.