  We clarify the status of two known solutions to the 5-dimensional vacuum
Einstein field equations derived by Liu, Mashhoon & Wesson (LMW) and Fukui,
Seahra & Wesson (FSW), respectively. Both 5-metrics explicitly embed
4-dimensional Friedman-Lemaitre-Robertson-Walker cosmologies with a wide range
of characteristics. We show that both metrics are also equivalent to
5-dimensional topological black hole (TBH) solutions, which is demonstrated by
finding explicit coordinate transformations from the TBH to LMW and FSW line
elements. We argue that the equivalence is a direct consequence of Birkhoff's
theorem generalized to 5 dimensions. Finally, for a special choice of
parameters we plot constant coordinate surfaces of the LMW patch in a
Penrose-Carter diagram. This shows that the LMW coordinates are regular across
the black and/or white hole horizons.
