Learn Farsi: من چهار پنج شاخه گل سفید خریدم. - I bought four or five stems of white flowers.

You do not need a word for 'or' here! Placing two consecutive numbers right next to each other, like چهار پنج (chahâr panj), automatically creates an estimated range. Adding the word for 'or', یا (yâ), is not grammatically required for this structure and would actually sound less natural.

Why is the word شاخه used before the flowers?

While شاخه literally translates to 'branch', it functions here as a counting word (or classifier) for objects with long stems, like flowers. You could technically use the generic counter تا (tâ), but using specific classifiers like شاخه makes your Farsi sound much more advanced and precise.

Since I am buying multiple stems of flowers, why aren't the words for stem and flower pluralized?

This is an important rule to remember: in Farsi, whenever a noun follows a number or a counting word, both the counting word and the noun itself must remain strictly singular. This rule still applies even when the number is an estimated range like چهار پنج.

Should there be an Ezafe linking the counting word شاخه and the noun گل?

No, you do not use an Ezafe between a counting word and the noun it counts. Just as you say دو لیوان آب (two glasses of water) without an Ezafe, you say پنج شاخه گل without one. However, there is an Ezafe between the noun گل and the adjective سفید (gol-e sefid) because adjectives always require one.