Yes, that's fine. English speakers regularly use "handful" to mean "about five".
As a random example I googled "handful of buildings" and got >700,000 hits, e.g. "Charnley-Persky House is one of a handful of buildings that display the combined talents of Louis Sullivan and Frank Lloyd Wright".
You can even have "a handful" of non-physical things: "a handful of ideas" gets almost 5 million hits on Google, e.g. "We started with a handful of ideas that sprung out of our collective experiences on social media."
To me (native English a la USA) apples are in a sort of uncanny valley between things that could in fact be measured by the physical handful, like peanuts, and things that couldn't -- buildings being way off the charts, obviously.
Same. A single apple, as found in the grocery store, is about one handful. Once you start talking about things much bigger than what an average human hand can hold then "a handful" does work as a synonym for "a few things" - probably less than ten.
As an American English speaker, I have never come across context where a handful means about five. Handful has meant a relatively small amount, with the actual quantity always depending on the context of the item being discussed.
The parent says "about five" because you have to choose to say "a handful" over "a few" or "several" or "a dozen or so" or just "many." Five is the sweet spot where none of those other terms apply.
Never really thought about this, but I wonder whether "handful" also is roughly equivalent to "number you can count on one hand" (ie, around 4 or 5 if counting with fingers).
As a random example I googled "handful of buildings" and got >700,000 hits, e.g. "Charnley-Persky House is one of a handful of buildings that display the combined talents of Louis Sullivan and Frank Lloyd Wright".
You can even have "a handful" of non-physical things: "a handful of ideas" gets almost 5 million hits on Google, e.g. "We started with a handful of ideas that sprung out of our collective experiences on social media."