Learn Farsi: بوی بدی در پنیر کهنه به وجود آمد.

When a noun is followed by an adjective in an Ezâfe chain, the indefinite -i suffix (meaning 'a' or 'an') attaches to the very end of the phrase. Therefore, instead of adding it to بو (smell), it attaches to بد (bad), creating بوی بدی (a bad smell).

What exactly does the verb به وجود آمد mean here?

The compound verb به وجود آمدن literally means 'to come into existence.' The word وجود means 'existence,' so in the context of a smell or a new situation, it translates smoothly to 'arose,' 'developed,' or 'formed.'

Could I use قدیمی instead of کهنه to say the cheese is old?

It would sound unnatural. In Farsi, قدیمی is generally used for things that are historically old or vintage, like an old city or an old friend. کهنه is used for things that are physically aged, worn out, or stale, making it the right choice for aged food or old clothes.

How would I connect this to a consequence using therefore (بنابراین)?

You would use it to start the following clause. For example, you could say: بوی بدی در پنیر کهنه به وجود آمد، بنابراین آن را دور انداختم (A bad smell arose in the aged cheese, therefore I threw it away). This clearly links the earlier event to its consequence.