Comprehensive and Detailed In-Depth Explanation:

Understanding OSPF Areas and Route Propagation in the Network:

OSPF Area Types in the Question:

Area 0 (Backbone Area): Connects all areas and distributes routing information.

Area 1 (Standard Area): Regular OSPF area that can receive and forward external routes.

Area 2 (Totally NSSA - Totally Not-So-Stubby Area):

Does not allow external routes except for a default route injected by the ABR.

Area 3 (NSSA - Not-So-Stubby Area):

Allows external routes as Type 7 LSAs but does not accept Type 5 LSAs.

How External Routes Are Advertised in This Scenario:

R5 (in Area 3) imports 10.0.5.5/32 as an external route into OSPF.

Since Area 3 is an NSSA, the external route is advertised as a Type 7 LSA (not Type 5).

The ABR (R1) converts the Type 7 LSA into a Type 5 LSA and advertises it into Area 0.

Once in Area 0, this Type 5 LSA can be distributed to other areas except totally stubby or totally NSSA areas.

Route Distribution Analysis:

R5 (Area 3) → R1 (Area 0, ABR):

R5 generates a Type 7 LSA for 10.0.5.5/32.

R1 (ABR) converts this Type 7 LSA into a Type 5 LSA and injects it into Area 0.

R2 (Area 0) → R3 (Area 0):

Since Area 0 allows external Type 5 LSAs, R2 and R3 receive 10.0.5.5/32.✅ R2 and R3 have the route.

R6 (Area 1) → Connected to Area 0:

Area 1 is a common area, meaning it can receive external Type 5 LSAs.✅ R6 has the route.

R4 (Area 2 - Totally NSSA):

Totally NSSA areas do NOT accept Type 5 or Type 7 LSAs.

Instead, they receive only a default route from the ABR (R3).

Since R4 does not receive external routes explicitly, it does NOT have 10.0.5.5/32.❌ R4 does NOT have the route.

Final Conclusion:

✅ R2, R3, and R6 have the route 10.0.5.5/32.

❌ R4 does not have the route because Area 2 is a Totally NSSA and only gets a default route.

Thus, the correct answer is:

✅ R2, R3, and R6 have the route 10.0.5.5/32 in their routing tables.