Odpady komunalne są w pięciu pojemnikach.

Because odpady is grammatically plural. In Polish, the subject and the verb must agree, so plural odpady takes plural są.

This can feel strange to an English speaker because English often uses singular waste. But Polish usually expresses this idea with plural odpady, so są is the natural form.

Because adjectives in Polish must agree with the noun in number, gender, and case.

Here the noun is odpady, which is:

• plural
• nominative
• non-masculine-personal

So the adjective also has to be plural nominative non-masculine-personal: komunalne.

Compare:

• odpady komunalne
• not odpady komunalni

The ending -ni is used for masculine personal plurals, mainly groups of men or mixed-gender people, so it would be wrong here.

It is a fairly standard, official-sounding term for municipal waste or household waste.

• odpady = waste, refuse
• komunalne = municipal, relating to local public services / household waste collection

In everyday speech, people may also say śmieci, but odpady komunalne sounds more formal and technical.

Because w means in here and is used to show location.

The sentence describes where something is:

• są w pojemnikach = are in the containers

When w means location, it takes the locative case.

So:

• w pojemniku = in the container
• w pojemnikach = in the containers

Because the phrase comes after w, and w for location requires the locative case.

The numeral pięć changes form in some cases:

• pięć = basic form
• pięciu = used in forms such as locative

So:

• pięć pojemników = five containers
• w pięciu pojemnikach = in five containers

English numerals do not change like this, but Polish numerals often do.

Because pojemnik has to be in the locative plural after w.

Singular and plural look like this:

• pojemnik = container
• pojemniki = containers
• w pojemnikach = in the containers

So in w pięciu pojemnikach, both parts are adjusted to fit the grammar of the phrase:

• w requires locative
• pięciu matches that
• pojemnikach is locative plural

Because Polish marks location with a preposition plus a case ending.

Here:

• w = in
• location after w normally takes the locative

So the whole expression meaning in five containers is built as one locative phrase:

• w
  • pięciu
    • pojemnikach

This is a very common pattern in Polish:

• w domu = in the house
• w szkołach = in schools
• w pięciu pojemnikach = in five containers

Yes. That is also correct.

znajdują się means something like are located or are situated. It sounds a bit more formal or explicit than plain są.

So:

• Odpady komunalne są w pięciu pojemnikach = simple, natural
• Odpady komunalne znajdują się w pięciu pojemnikach = a bit more formal, more descriptive

Yes. Polish word order is more flexible than English word order.

The neutral order here is:

• Odpady komunalne są w pięciu pojemnikach.

But you could also say:

• W pięciu pojemnikach są odpady komunalne.

That version puts more focus on where they are.

The meaning stays basically the same, but the emphasis changes.

Because Polish has no articles. There is no direct equivalent of English a/an or the in normal sentences.

So odpady komunalne can mean:

• municipal waste
• the municipal waste

and w pięciu pojemnikach can mean:

• in five containers
• in the five containers

The exact interpretation comes from context.

Often yes, but the tone changes.

• śmieci = trash, garbage, everyday word
• odpady komunalne = municipal waste, more official/technical

So:

• Śmieci są w pięciu pojemnikach sounds more everyday
• Odpady komunalne są w pięciu pojemnikach sounds more formal, like signage, regulations, or public information

They are related, but not always perfectly interchangeable in every context.