Недаром бабушка советует выходить пораньше: сегодня мы действительно успели без спешки.

Here недаром means not for nothing, for good reason, or no wonder.

So Недаром бабушка советует... means something like:

• Grandma tells us to leave earlier for a reason
• No wonder Grandma advises leaving earlier
• Grandma isn’t saying that for nothing

A useful distinction:

• недаром = an adverb meaning for good reason
• не даром = literally not for free

Those are different expressions.

Советует is the present-tense form of советовать: to advise.

Russian often uses the present tense when talking about:

• a general piece of advice
• something someone regularly says
• advice that is still relevant now

So бабушка советует выходить пораньше suggests something like:

• Grandma advises leaving earlier
• Grandma keeps telling us to leave earlier
• Grandma says we should leave earlier

If the speaker wanted to refer to one specific past moment of advice, Russian might use посоветовала instead.

This is an aspect question.

• выходить = imperfective
• выйти = perfective

After советовать, Russian often uses the imperfective infinitive when the advice is general, repeated, or about a usual way of acting.

So советует выходить пораньше means something like:

• advises leaving earlier
• advises us to head out earlier as a rule

If the advice were about one specific occasion, выйти could also be possible:

• Бабушка советует выйти пораньше = Grandma advises us to leave a bit early this one time

So here выходить makes the advice sound more general or habitual.

Although выходить literally means to go out, in this context it usually means to leave home, to set off, or to head out.

So выходить пораньше is not just physically stepping outside. It means:

• to leave earlier
• to set out a bit earlier
• to head out early

Context decides the most natural English translation.

Пораньше means a bit earlier, somewhat earlier, or rather early.

It is related to раньше (earlier), but пораньше often sounds a little softer or more practical, like:

• leave a bit earlier
• try to head out earlier

Compare:

• раньше = earlier
• пораньше = a little earlier / nice and early

This по- form is very common in everyday Russian:

• побольше = a bit more
• поменьше = a bit less
• побыстрее = a bit faster
• пораньше = a bit earlier

The colon introduces an explanation or confirmation of the first part.

Structure:

• Недаром бабушка советует выходить пораньше:
  сегодня мы действительно успели без спешки.

The second part explains why Grandma’s advice makes sense:

• we left earlier
• as a result, today we had enough time and did not have to rush

In English, this might be written with a colon, dash, or even as two sentences. In Russian, the colon works well when the second part explains or justifies the first.

Действительно means really, indeed, or actually in the sense of confirming something.

Here it emphasizes that Grandma’s advice turned out to be correct:

• сегодня мы действительно успели = today we really did make it in time
• today we indeed had enough time

It strengthens the idea that the result confirms the advice from the first part.

Успели is the past plural form of the perfective verb успеть.

Успеть often means:

• to manage to do something in time
• to be in time
• to make it
• to have enough time

So мы успели means:

• we made it in time
• we managed
• we had enough time

The perfective aspect is important here because it shows a completed result: the goal was successfully achieved.

Very good question. Often успеть is followed by an infinitive:

• мы успели прийти
• мы успели добраться
• мы успели сделать это

But in this sentence, the infinitive is omitted because it is understood from context.

So сегодня мы действительно успели без спешки means something like:

• today we really made it in time without rushing
• today we had enough time and didn’t have to rush

Russian often leaves out an infinitive when the meaning is obvious.

Because the preposition без always takes the genitive case.

So:

• без
  • genitive
• спешка becomes спешки

без спешки literally means without haste, but in natural English it is usually:

• without rushing
• in no hurry
• without any rush

This phrase is very common in Russian.

Russian word order is flexible, so the basic meaning would still be clear in other orders too. But the chosen order affects emphasis.

In this sentence:

• сегодня sets the time frame first
• мы gives the subject
• действительно emphasizes confirmation
• успели gives the main result
• без спешки adds the manner

So the order sounds natural and highlights:

Today, we really did manage, and we did it without rushing.

Other orders are possible, but they may shift focus slightly. For example:

• Мы сегодня действительно успели без спешки = a bit more neutral
• Мы без спешки действительно успели сегодня = less natural in this context, and the emphasis changes

So the word order is not rigid, but it is meaningful.

Both are possible, but leave earlier is usually better English here.

A more literal translation of выходить is go out, but in this context the real idea is:

• leaving home earlier
• setting off earlier
• heading out earlier

So leave earlier sounds more natural to an English speaker.

That is a common issue in Russian: the most literal verb translation is not always the most natural one in context.