I think I can only reasonably base my choices on my last visit, which sadly rules out 2 of the favourite zoos of my lifetime, London, which has fallen from the position for decades and Whipsnade, possibly only on my last visit a few weeks ago which I found a bit disappointing!If you visited at the time you liked it (eg 1970's) that is fine. However if you want to clarify that it would not apply now you can make a short comment following your listing.
1 Berlin Tierpark (2017)
2 Zoo Berlin (2017)
3 Zoo Duisburg (2018)
4 Chester Zoo (Last visited 2018)
5 Hamerton Zoo ( last visit a week ago and is better every time I go, approximately 4 times a year on average)
Honourable mentions in addition to ZSL would be Yorkshire Wildlife Park currently , late 70s Marwell, Cologne last year (it doesn't make the top 5, because though some parts were excellent, some I thought were very poor for a zoo of its standing), Colchester ( though I think that has started a decline).