Is there an English idiom “in threes and fives” to describe arriving, gathering, or leaving of people in a pair, trio, or group in succession?

We say ‘san-san-go-go – 三三五五’ in Japanese to describe the status of people coming, arriving, gathering, going, or leaving in a pair, trio, or group in succession in such a way, People gathered in the square ‘san-san-go-go.’ ‘San’ means three in Japanese. ‘Go’ means five, and ‘san-san-go- go’ is used adverbially.

I know “by ones and twos” is applied to the case more than “by one and one.”

When I consulted New Japanese English Dictionary published by Japanese publisher (Kenkyusha Publishing), I found the translation – ‘in threes and fives.’

I suspect if this is a literal translation of 3-3-5-5, and not standard English phrase.

Is there an idiom or phrase to express the status of people coming (arriving) and going (leaving) in the pack of three-to five individuals to a place incessantly?

You're right in your suspicion that "in threes and fives" is a literal translation and not idiomatic. You mention "in ones and twos," which is what I would have suggested as an answer. If you're looking for a phrase that means people coming or going specifically in groups of three to five, I can't think of one, but you could try:

The people were coming (going) in dribs and drabs. ("A series of negligible amounts.")

This gives a sense of disorganization, of a few here, a few there.

But in ones and twos is idiomatic and I would suspect quite satisfactory for most purposes: in small numbers.

Finally, it would be perfectly acceptable (though not idiomatic) to say

The people were coming (going) in groups of three to five.

It's not really idiomatic, but it is a common utterance:

a few at a time

few : 1. An indefinitely small number of persons or things

The dictionary says indefinitely small and I think this covers the 3-5 range nicely, because two would be 'a couple', or we have 'in ones and twos' as mentioned in other answers for those specific cases.

There was a wonderful series of humorous underground papers by Paul Postal back in the early 1970s called "Linguistic Anarchy Notes", which dealt with syntactic problems that couldn't be handled then (and can't be handled now, either) by formal generative theories.

Like the pronoun reference in sentences like
- The alligator's tail fell off, but it grew back.
- His house burned down, but he eventually rebuilt it as a Georgian mansion.
I.e, exactly what does it refer to in these sentences?

One paper in this series (none of which are available on the Web, which is yet more shame for academic linguists) was entitled "Plus One, or How About Arithmetic?", and dealt with grammaticality facts of the following sorts:

• Two or three of them are coming.
• *Two or seventeen of them are coming.
• They're arriving by ones and twos.
• *They're arriving by threes and fives.
• Six or seven of us voted against it.
• *Seven or six of us voted against it.
• There are ten or twelve of them.
• *There are ten or eight of them.
• There are a dozen or two of them.
• *There are a dozen or six of them.

The generalization here is that the rules for combining number words into rough quantificational modifiers are extremely complex, and involve how close the numbers are to one another in sequence, and precisely how close the estimate is intended to be. This is the sort of thing that generative linguistics is not very good at.

When a group of people who are all meant to be in one place arrive in small groups over a period of time, the common description is "in twos and threes". I wonder if Japanese groups really are larger on average?

The term dribs and drabs is also sometimes applied to people moving in and/or out of a space.

An Australianism that is typically applied to the movement of a large group of children is like Brown's cows to convey the apparently pointless meandering of small groups that will eventually result in everyone arriving at the designated place.