May 5th is the Yom HaZikaron (Day of Remembrance), when Israelis commemorate fallen soldiers and civilians who died in terrorist attacks. Most places around Tel Aviv are closed on that day, and a large ceremony is held in Rabin Sqaure (כיכר רבין).
The following day is Yom Ha’Atzma’ut – Israeli independece day. In fact, celebrations start on the evening of May 5th. The city centre (Ibn Gabirol St., Rabin Square and the areas surrounding it) will probably be crowded, but getting there will give you the best view for the traditional firework display at around 8pm. On that evening, you can find street parties on most main streets (Ibn Gabirol, Rothschild Boulevard, Nachalat Binyamin, to name a few), and on the day itself, you will probably see Israelis in vast numbers BBQing on every possible corner of the city, as tradition goes. On top of all that, if you get to Jaffa, you might expect to see more Palestinian flags, as Israeli Independence Day – commemorating the day the State of Israel was founded – is also the Palestinian Nakba – commemorating the hunderds of thousands of Palestinians who became refugees in the 1948 war. An interesting place to go to on that night is Jaffa’s Anna Loulou Bar.