Step 1: Understanding the Concept:
Isomerism in coordination compounds arises when compounds have the same molecular formula but different arrangements of atoms.
Step 2: Detailed Explanation:
Linkage isomerism occurs when an ambidentate ligand is present in the complex.
An ambidentate ligand is a ligand that has more than one donor atom but coordinates through only one atom at a time.
In the given complexes, the ligand is the nitrite ion ($NO_2^-$).
1. In $[Co(NH_3)_5(NO_2)]^{2+}$, the ligand is bonded through the Nitrogen atom (nitro-N).
2. In $[Co(NH_3)_5(ONO)]^{2+}$, the ligand is bonded through the Oxygen atom (nitrito-O).
Since the difference is in the mode of attachment (linkage) of the ligand to the metal, they are linkage isomers.
Step 3: Final Answer:
They are linkage isomers.