Please be aware that when you see sharks, quite often you have a strong current. Strong current and AOW with 5 dives is a clear no........no.
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That is quite wrong. As with anything that requires skill, the most dramatic improvements happen early. The better you get, the harder you have to work to reach the next level. The difference between having 10 or 30 dives will be very pronounced whereas the difference between 1000 dives and 1020 dives will generally be negligible.
As mentioned, you can see tiger sharks elsewhere if you won't make it back to Fiji. I also believe that the odds of seeing the tigers on this Fiji dive are depending on the season and actually not that great. Other options mentioned above have a higher success rate. Nonetheless, none of theses operations will hold your hand. You will have to be a reasonably experienced diver to go on a tiger shark dive and videoing as you mention adds another level of task loading. They also like to bump you, especially at tiger beach, and sometimes quite insistently. Your diving skills should be on auto pilot to competently deal with large sharks (and camera equipment). How many dives that takes varies by individual but 5 or 10 or 20 is not enough.