This year Yom HaZikaron and Yom Ha’atzmaut were moved forward by one day each, so that Yom Ha’atzmaut was celebrated on 4 Iyar. Since the actual date of the chag is 5 Iyar, should we have said/omitted tachnun this year on 5 Iyar?

According Rav Zalman Melamed and the Chief Rabbinate of Israel, one should not recite Tachanun on the fifth day of Iyar whether Yom Ha'atzmaut is celebrated on this day or not. Additionally, Tachanun is not recited on the day Yom Haatzmaut is actually celebrated, regardless of the date on which it is celebrated.