I've been to Croatia twice: once in early October, once (more recently) in early May.
May and October might be considered "shoulder shoulder season." There will be fewer options (fewer excursions, earlier closing hours, etc.), but I don't think it's accurate anymore to say that all of Croatia is "dead as a doornail" in these months. SOME places are though - especially the islands, as I understand it. My only experience there was on Korcula in October, and it was indeed pretty dead - restaurants were open at night but it was hard to tell until you walked up to the place, because there were few people out. I get the idea it's kind of like that in May too.
Dubrovnik, on the other hand, is not going to be "dead" in May, probably not in April either. It gets a ton of cruise ship passengers now - which is mostly a curse for other tourists, because the place gets mobbed in the day time. Zadar had an event going on in May the weekend I was there and most places were booked and the city was crowded. Trogir was not dead but not busy. Rovinj was about the same: not dead but not busy. Plitvice was busy in May but not mobbed. Zagreb being the capital is not a big tourist destination, so the time of year you visit there should be irrelevant.
On the upside, it's much easier to find places to stay even on short notice. I booked most of my May accommodations at the very last minute (having an internet device was essential - and I was driving). Sometimes I had nothing booked until the morning of arrival. Other than Zadar, I had no problem at all finding last-minute lodgings and still got great prices. And driving was cheap and easy; rental car was cheap, roads on the coast especially were not busy at all with tourist traffic.
On the downside, the ocean is probably too cold for swimming in early May. And the weather might be more rainy than in the summer/fall - though the May I was there I had almost no rain. (Sadly, I saw mostly clouds at sunset, so I only saw the sun set into the ocean once, in Rovinj - something magical I enjoyed several times on my first visit to Croatia in October, when most days were cloudless.)
I guess if I were you, I'd post a potential itinerary for review and look at each spot and see what might be a problem for you to visit in May. I probably wouldn't do an island-heavy itinerary or one that focuses on "sun and fun at the beach," but otherwise I'd probably go for it.