Learn Italian: Il negozio è aperto cinque o sei giorni.

No. In Italian, almost all numbers are invariable, meaning their endings never change, no matter what they are describing. The only exception from 1 to 10 is the number one (uno, una). So you just say cinque giorni and sei giorni.

We are talking about multiple days, so why does aperto have a singular ending?

Because aperto (open) describes il negozio (the shop), which is a masculine singular noun. The shop is what is open, not the days. If we were talking about multiple shops, it would be I negozi sono aperti.

Why does giorni end in -i?

Giorni is the plural of giorno (day). As a quick refresher: in Italian, most masculine nouns that end in -o in the singular change their ending to -i in the plural.

Is o the standard word for 'or'?

Yes! The single letter o means 'or' in Italian. It connects two alternatives, just like in the English phrase 'five or six'.