Yokohama Hakkeijima’s penguins are spread across different areas.
Aqua Museum’s LABO4, “Animals Living in the Icy Sea,” officially lists chinstrap penguins, king penguins, gentoo penguins, and Adélie penguins. Fureai Lagoon’s activity page mentions Cape penguins, meaning African penguins.
So “five penguin species” can be true, but only if you keep clear that they are in different areas.

What to see
The Aqua Museum focus is Antarctic and subantarctic species. Adélie penguins are small and clean-lined, chinstrap penguins have the black line under the chin, king penguins dominate the scene with height, and gentoo penguins are fast in the water.
Fureai Lagoon has a different rhythm. The official English page lists paid or performance-style programs with penguins, seals, and otaria, and it also has an African penguin parade and performance. It leans more toward interaction and education than simple viewing through glass.
If you want a high-density penguin facility in Japan, Hakkeijima is useful to compare with Nagasaki Penguin Aquarium. Nagasaki is more specialized; Hakkeijima feels more like a large sea-island leisure park.
For a quieter Kanto city-aquarium answer, Sumida Aquarium gives a shorter and more urban contrast.

How to plan it
Hakkeijima is not the kind of place you briefly pass through in an ordinary neighborhood. It is a whole leisure island on the water, and the aquariums, rides, restaurants, and shops naturally stretch the visit.
If you are only going for penguins, decide first whether to buy the Aqua Resorts Pass or a one-day pass. Check separately whether interaction programs cost extra and whether they require advance booking.
A day trip from Tokyo is possible, but do not make the return too tight. Transfers on the Seaside Line, Keikyu, or JR can take more energy than they look.

Penchan Says
Hakkeijima works well for people who want to see several penguin species in one day.
It is just not a single penguin house. It is a sea-island leisure park that can scatter your attention. Mark the penguin points first, or the rest of the island will carry the whole day away.
References
FAQ
How many penguin species are at Yokohama Hakkeijima Sea Paradise?
The guide organizes the official material as five species: chinstrap, king, gentoo, and Adélie penguins in Aqua Museum, plus Cape/African penguins in Fureai Lagoon.
Are all Hakkeijima penguins in one exhibit?
No. Aqua Museum focuses on Antarctic and subantarctic cold-water species, while Fureai Lagoon leans toward interaction, education, and African penguin programs.
What ticket should I check if I only want penguins at Hakkeijima?
The article suggests deciding first between an Aqua Resorts Pass and a one-day pass, then checking whether interaction programs cost extra or require advance booking.