Kirby and Siebenmann obstruction for $D \neq 5$?

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In 1984 old Book "Instantons_And_Four-Manifolds_Instantons and 4-Manifolds" in p.1 by Dan Freed and Karen Uhlenbeck: it says

"In 1968 Kirby and Siebenmann determined that for a topological manifold M of dimension at least five ($D=5$). there is a single obstruction $$a(M) \in H^4(M;Z_2)$$ to the existence of a PL structure."

My question is that are there examples outside dimension D=5 have this obstruction $ a(M) \in H^4(M;Z_2)$? For example

  • at $D=4$, say $E_8$ manifolds?

  • at any $D\geq 4$, say $E_8 \times T^{D-4}$ manifolds?

If yes, of if there are known examples, why Dan Freed and Karen Uhlenbeck only stated $D=5?$