The knee-jerk reaction to the question titling this post is “5 Iyar”, but knee-jerk reactions are often wrong. The Israeli Rabbanut policy is not to celebrate Yom ha’Atzmaut on 5 Iyar when the date falls immediately before/after Shabbos so as to minimize the risk of chilul Shabbos. This year, although 5 Iyar is Monday, since Yom ha’Atzmaut always follows Yom haZikaron and Yom haZikaron would fall out immediatly after Shabbos, the Rabbanut pushed Yom haZikaron to Monday, 5 Iyar, and Yom ha’Atzmaut will be celebrated Tuesday, 6 Iyar. This also somewhat obviates the problem for those who will fast BH”B on Monday and feel that adding a celebration and/or hallel to tefillah would be inconsistent with the spirit of the ta’anis (I seem to recall this issue coming up in the YU Bais Medrash).
Whether or not American (or other diaspora communities) should schedule their celebrations for 6 Iyar or keep to the date of 5 Iyar always seems to be a matter of debate (there seems far less concern for celebrations creating chilul Shabbos here, esp. with respect to Yom haZikaron). I noticed the OU website lists the dates as matching the Rabbanut’s decision, and after a bit of googling I found that the last time this occurred (2004) R’ Gedalya Dov Schwartz originally said to celebrate on 5 Iyar (Monday) but then in response to a request from a Rabbanut advised the RCA to celebrate on 6 Iyar. I heard in the name of R’ Ahron Soloveitchik that 5 Iyar should always be celebrated. Of course, this entire discussion is moot if you don't celebrate in some way or other and see no theological significance to the re-establishment of the State, but that’s a discussion for another post.