Thank you for reaching out.

In general, the 5-day minimum is treated strictly for Ashkenazi women, and a hefsek on day 4 is permitted only in very extenuating circumstances. 

If you are able to get to a mikveh on the night of Shavuot, you should perform your hefsek on day 5 as usual, and schedule your immersion for Shavuot night. This is the ideal scenario in this situation. You may want to see our pages on mikveh on Yom Tov, and on makeup and mikveh on Yom Tov, for more information.

If you will be in walking distance from a mikveh but it is a long walk, it might be possible for you to drive or get a ride to the mikveh before sunset, and walk back after you immerse. That way, you would only need to walk one way. In that scenario, you would light Yom Tov candles from an existing flame after you get home.

If you don't have access to a mikveh on Shavuot, and delaying immersion would mean delaying for 2 nights until Motzai Shabbat, there is room to permit immersing on erev Shavuot in the afternoon (again, having performed the hefsek on day 5), on condition that you do not see your husband from the time you immerse until after nightfall. This should be arranged in advance with the mikveh attendant. 

Only if neither of the above scenarios are possible, and you are able to actually get an acceptable hefsek on day 4, given the extenuating circumstances in this situation there is room to permit a day 4 hefsek. You would be scheduled to immerse the night before chag.

Please feel free to get back to us with any further questions. 

Chag sameach!