Is it obligatory to fast five days every time the vowed sin is committed, and is it permissible to change the vow from fasting to paying a sum of money?

This vow is considered a "vow of obstinacy" (nadhir lajaj), and according to the most preponderant opinion, it entails an expiation for breaking an oath (kaffarat yamin), or one may choose between expiation and fulfilling the vow.

One must hasten to repent. The one who made the vow chooses between performing what was vowed or offering an expiation for breaking an oath, and both are sufficient.

If the vow was made in a form that implies repetition (such as: "every time I do this thing"), then the vow is continuous, and expiation or fasting becomes obligatory every time the action is repeated.

If the vow does not imply repetition (such as: "if I do such and such") and repetition of the vow was not intended, then the vow is dissolved with the first instance, and only one expiation is required.