I noticed when the animation occurs the style is being set to:
transition: none;
-webkit-transition: none;
I assume ngAnimate sets these style properties during it's processing and the other browsers are unaffected by them during the brief moment they are set but when chrome sees them it immediately completes the animation as though no transition was applied.
So to fix your problem you just need to ensure these properties get ignored by setting your properties as !important:
transition: height 5s !important;
-webkit-transition: height 5s !important;
Which can be seen working in the plnkr here