I would say. The beach is a five-minute walk from my home The beach is five minutes' walk from my home

Ah, if only the beach were indeed just five minutes from my home!

You have the grammatical structure right, however whether you say house or home, depends on what kind of building you live in. A house is a particular type of building, whereas a home is a place where someone lives, so a home could be anything from an apartment to a boat, as long as someone lives in it. Most people I believe would say "the beach is 5 minutes from my place." But house and home are just as acceptable.

It's fine and absolutely natural. You might want to be more precise about the 5 minutes. For example, It's a five-minute drive from my home. or It's a five-minute walk from my home. or It's a five-minute bus ride from my home. But otherwise, your sentence is perfect.

You can also just say: The beach is five minutes away.