I noticed that people sometimes use fuchzehn and fuchzig instead of fünfzehn and fünfzig. Is there a certain reason or is this just dialect?
It's just dialect. Only "fünfzehn" and "fünfzig" are correct.
The pronunciation fuchzehn (as well as fuffzehn) is a regional variant of the standard German word fünfzehn. It is mainly used in the south-east of the German language area. The area of distribution is shown in a linguistic map of the linguistic atlas Atlas zur deutschen Alltagssprache:
Ich kenne nur fuffzig und fuffzehn (Dialekt), nicht "fuchzig" oder "fuchzehn".