Nie mogę znaleźć śrubokręta, więc fachowiec pożycza mi swój.

Because mogę means I can / I am able to, and after móc Polish normally uses an infinitive:

• mogę znaleźć = I can find
• nie mogę znaleźć = I can’t find

So this works very much like English can + verb.

Because in Polish, a direct object often changes to the genitive in a negative sentence.

Compare:

• Mogę znaleźć śrubokręt. = I can find the screwdriver.
• Nie mogę znaleźć śrubokręta. = I can’t find the screwdriver.

Here:

• śrubokręt = nominative / accusative singular
• śrubokręta = genitive singular

This is a very common pattern after negation.

Polish has no articles, so there is no direct equivalent of English a/an/the.

So śrubokręta can mean:

• a screwdriver
• the screwdriver

The exact meaning depends on context.

Mi is the dative form of ja here, meaning to me / for me.

In this sentence:

• fachowiec pożycza mi swój = the professional is lending me his own

Why mi and not mnie?

• mi is the short, unstressed form
• mnie is used more for emphasis, contrast, or after prepositions

So here mi is the normal, natural choice.

It can mean either, depending on the structure.

• pożyczyć / pożyczać coś komuś = to lend something to someone
• pożyczyć / pożyczać coś od kogoś = to borrow something from someone

In your sentence, we have mi (to me), so it means:

• fachowiec pożycza mi swój = the professional lends me his own

That is a very common point of confusion for English speakers.

Because swój is the reflexive possessive, used when the possessor is the same as the subject of the sentence.

Here the subject is:

• fachowiec = the professional / tradesman

And it is his own screwdriver that he is lending. So Polish normally prefers:

• fachowiec pożycza mi swój = the professional lends me his own

If you used jego, it could sound less natural here or suggest someone else’s screwdriver.

Because Polish often omits a repeated noun when it is obvious from context.

Here swój really means:

• swój śrubokręt = his own screwdriver

But since śrubokręt was already mentioned, Polish can just say swój.

This is similar to English his own one or simply his, although Polish does this more freely.

Because swój must match the omitted noun śrubokręt.

The hidden full phrase is:

• pożycza mi swój śrubokręt

Since śrubokręt is:

• masculine singular
• inanimate
• direct object

the correct accusative form is swój.

If the noun were different, the form would change:

• swoją wiertarkę = his own drill
• swoje narzędzie = his own tool

Pożycza is the present tense of the imperfective verb pożyczać.

Depending on context, it can mean:

• lends
• is lending

In this sentence, English would probably translate it as is lending me his, because it sounds like a current situation.

If you used the perfective verb pożyczyć, the future form would be:

• pożyczy mi swój = he will lend me his own

So this is also about aspect, not just tense.

Not completely. Polish word order is fairly flexible.

This sentence has a very natural order:

• Nie mogę znaleźć śrubokręta, więc fachowiec pożycza mi swój.

It flows like:

1. problem
2. result

You could change the order a bit, for example:

• Nie mogę znaleźć śrubokręta, więc mi fachowiec pożycza swój.
• Nie mogę znaleźć śrubokręta, więc fachowiec mi pożycza swój.

But the original version sounds neutral and natural.

Więc means so, therefore, or thus.

It introduces the consequence of the first clause:

• Nie mogę znaleźć śrubokręta = I can’t find the screwdriver
• więc = so
• fachowiec pożycza mi swój = the professional lends me his own

It is a very common connecting word in everyday Polish.

A rough guide:

• ś = a soft sh
• ó = oo
• ę before t is often pronounced close to en
• ch = a throaty h sound
• wie in fachowiec sounds roughly like vye

Approximate pronunciations:

• śrubokręta ≈ shroo-bo-KREN-ta
• fachowiec ≈ fa-HO-vyets

These are only approximations, but they are good enough to help you start saying them.