Нам пора бы выходить пораньше, чтобы после работы успевать в зал без спешки.

Because пора normally goes with the dative case, not the nominative.

So:

• нам пора = it’s time for us
• literally, something like to us, it is time

This is a very common Russian impersonal pattern:

• мне пора = it’s time for me
• тебе пора = it’s time for you
• нам пора = it’s time for us

So мы пора would be ungrammatical.

Пора by itself means it’s time.

Adding бы makes it softer and more tentative, and often gives a sense of:

• we really should
• it would be a good idea to
• it’s probably about time

So:

• Нам пора выходить пораньше = It’s time for us to leave earlier
• Нам пора бы выходить пораньше = We really should start leaving earlier

The particle бы often adds a slight nuance of suggestion, mild regret, or delayed action. It can sound like the speaker feels this should already have been happening.

Because the sentence is talking about a repeated or habitual action, not one single completed event.

• выходить = to leave, to be leaving, to leave regularly
• выйти = to leave once, to go out and complete that action

Here the idea is:

• we should make a habit of leaving earlier
• so that after work we can regularly make it to the gym without rushing

That is why imperfective выходить fits well.

If you used выйти, it would sound more like a single specific occasion.

Пораньше means a bit earlier or somewhat earlier.

Compare:

• раньше = earlier
• пораньше = a little earlier / somewhat earlier

This по- form is very common in conversational Russian and often makes the comparison feel less absolute and more practical.

So:

• выходить раньше = leave earlier
• выходить пораньше = leave a bit earlier

In this sentence, пораньше sounds natural and idiomatic.

Because the sentence describes a regular goal, not a one-time result.

• успевать = to manage to, to have enough time, on a repeated or ongoing basis
• успеть = to manage to do something once, successfully complete it in time

Here the meaning is:

• leave earlier as a habit
• so that after work we can consistently make it to the gym without rushing

So imperfective успевать is the natural choice.

Compare:

• чтобы успеть в зал = so as to make it to the gym this one time
• чтобы успевать в зал = so as to be able to make it to the gym regularly

The preposition после always takes the genitive case.

So:

• работа = work
• после работы = after work

This is a fixed grammatical rule:

• после урока = after class
• после обеда = after lunch
• после работы = after work

In this sentence, после работы means after work / after the workday.

В зал means to the gym here.

Grammatically:

• в
  • accusative is used for motion into a place
• зал is the accusative form here, and for this noun it looks the same as the dictionary form

So:

• в зал = into/to the gym
• в зале = in the gym

As for meaning, зал literally means hall, but in everyday speech it can refer to:

• a gym
• a workout room
• a fitness hall

Depending on context, в зал often means to the gym.

Без спешки means:

• without rushing
• without hurry
• in an unhurried way

The preposition без always takes the genitive case, so:

• спешка = rush, haste
• без спешки = without haste

This phrase does not necessarily mean slowly. It means doing something without time pressure.

Russian often leaves out the subject when it is clear from context or when the structure is impersonal.

This sentence is built around the impersonal expression нам пора бы, so мы is not needed.

The sentence already tells you who is involved through нам:

• нам = for us / to us

Russian very often prefers this kind of compact structure over explicitly stating мы.

Yes, Russian word order is fairly flexible.

The given version is natural:

• Нам пора бы выходить пораньше, чтобы после работы успевать в зал без спешки.

But other arrangements are possible, for example:

• Нам пора бы пораньше выходить, чтобы после работы успевать в зал без спешки.
• Чтобы после работы успевать в зал без спешки, нам пора бы выходить пораньше.

The basic meaning stays the same, but the emphasis shifts slightly.

In the original sentence, после работы is placed before успевать to frame the time context clearly: the goal is to make it to the gym after work.

It sounds mostly natural and conversational, especially because of:

• пора бы
• пораньше

These make it sound like everyday spoken Russian rather than very formal written language.

A slightly more neutral version could be:

• Нам нужно выходить пораньше, чтобы после работы успевать в зал без спешки.

That sounds more straightforward: we need to leave earlier.

The original version has a softer, more reflective tone: we really should be leaving earlier.