Beşe on kala geldim.

Because beşe is the dative form of beş (five).

In Turkish, when you tell time with minutes remaining until an hour, the upcoming hour is put in the dative:

• beşe on kala = when ten minutes remained to five
• literally: to five, ten remaining

So:

• beş = five
• beşe = to five

This is one of the standard patterns used in Turkish time expressions.

on kala means with ten minutes remaining or more naturally ten minutes before.

It comes from the verb kalmak, which means to remain / to be left.
Here, kala is a special form meaning something like with ... left.

So:

• beşe on kala = with ten minutes left to five
• natural English equivalent: at ten to five

This pattern is commonly used when saying that something happened at a certain time:

• Altıya beş kala çıktım. = I left at five to six.
• İkiye çeyrek kala aradı. = He/she called at quarter to two.

This is a very common question.

Turkish usually uses var when simply stating what time it is:

• Saat beşe on var. = It is ten to five.

But when you say that something happened at that time, Turkish often uses kala:

• Beşe on kala geldim. = I arrived at ten to five.

So the difference is roughly:

• var → for telling the time itself
• kala → for saying an action happened with that amount of time left before the hour

You may also hear saat beşe on kala with saat included, especially for clarity.

Geldim means I came or I arrived.

It comes from:

• gel- = come
• -di = past tense
• -m = first person singular (I)

So:

• gel-di-m = I came

This is why Turkish does not need the subject pronoun ben here. The verb ending already tells you the subject is I.

Because Turkish usually leaves out subject pronouns when the verb already shows who the subject is.

In geldim, the ending -m already means I. So ben is unnecessary unless you want emphasis.

Compare:

• Geldim. = I came.
• Ben geldim. = I came. / It was me who came.

So Beşe on kala geldim is perfectly normal without ben.

The word order is normal in Turkish.

Turkish often puts time expressions before the verb, and very often near the beginning of the sentence:

• Beşe on kala geldim.
• Dün geldim. = I came yesterday.
• Sabah erkenden çıktık. = We left early in the morning.

The verb usually comes at the end in Turkish, so geldim being last is exactly what you would expect.

Yes, absolutely.

Both are possible:

• Beşe on kala geldim.
• Saat beşe on kala geldim.

Adding saat makes the time expression a little more explicit, similar to saying at ten to five more clearly. In many everyday contexts, though, Turkish simply leaves saat out.

Yes.

Instead of the remaining to the hour style, Turkish can also use a digital-style clock expression:

• Dört ellide geldim. = I came at 4:50.

So these are equivalent in meaning:

• Beşe on kala geldim.
• Dört ellide geldim.

The first sounds like traditional clock-based time phrasing; the second is more like reading the numbers directly.

Use the same pattern:

[upcoming hour in dative] + [minutes] + kala + [verb]

Examples:

• Altıya beş kala çıktım. = I left at five to six.
• Üçe yirmi kala aradılar. = They called at twenty to three.
• On bire çeyrek kala uyandım. = I woke up at quarter to eleven.

A few useful minute words:

• beş = five
• on = ten
• yirmi = twenty
• yirmi beş = twenty-five
• çeyrek = quarter

It means ten to five, not five to ten.

This is important because Turkish builds the expression around the next hour:

• beşe = to five
• on kala = with ten left

So Turkish is saying:

• to five, ten remaining

That equals 4:50, or ten to five in English.

In isolation, gelmek means to come.
But in a sentence like this, English often prefers arrive:

• Beşe on kala geldim. = I arrived at ten to five.

So grammatically it is from come, but in natural English the best translation may be arrive, depending on context.