The first one sounds better. You might say, "I've set a reminder for the 20th of every month for the next five months." The "20th of the next 5 months" is confusing because it could suggest that there may be one 20th related to the next 5 months, which doesn't really make sense. For example, if you said "the first of the next five months" it would mean the first month out of the next five, not the first day of each of the next five months.
- For Teachers