Ooh, if 5 was your intro to the series, then you're in for a treat. If you enjoyed the darker themes of 5 and/or want to be able to play as a female MC, then definitely play 3 next. It's my favourite for that reason, and also the game I have the most ships for by faaar, haha. P3 has the advantage that you can theoretically finish every social link etc in one playthrough, as well. Otoh, if you want something a little (just a little!) more lighthearted, and on a larger scale (like P5), then play 4. I love all three, but 3 is the one I've replayed the most, because of its characters.

ETA: I haven't played 1 or 2, but I've heard that they're really quite different to the more recent ones - the social links etc all started with P3, afaik.