*Nod* Kiwiactrss has some good suggestions
Another thing which you, like I did, might realize once the zoo gets big enough is that the zookeepers aren't really too dedicated when it comes to their job. I had stuck at 4 - 4½ stars, and in order to finally get up to 5, I did the following:
-Make super-sure that all exhibits have the right plants, flowers etc (only from correct continent)
-Placed out guides. I didn't have a million but I tried to have as many as I could afford
-Re-shaped the exhibits. If the normal shape is like this:
|-----|
|......|
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I made it more like this:
|--|.|-|
|...--..|
|------|
Sorry, not the best way to explain it
But basically the guests could walk "into" the exhbibit. That way they get a closer look to the animals no matter where they are located at the time. Those areas I of course filled with donation boxes, those things they stand under (sorry, english isn't my first language, don't remember what they're called XD) and binoculars. A guide too if it can fit in somewhere. They took a little bit of time before the guests saw the new formations but they seemed to love them.
-Make sure the animal has a lot to play with, as someone mentioned. Guests are more happy when the animals are doing something fun.
-Once you are sure everything else is right, go on a round to clean every exhbibit, since chances are the keepers haven't done the best job. Fill up bowls, clean the animals, clean the exhibits etc. I found this can make a really big difference.
-If one animal craves too much attention/soils its exhibit too much, it can be an idea to get rid off it. My peafowl drove me nuts, so close to the end I exchanged them for some other animal (don't remmember which it was, though) which meant I didn't have to run back and clean that exhibit as often.
Once you get 5 stars, save your game and try to cancel animals until you get it. If you don't get it, it could be a start to go back to the main menu, open the file again and try again until you get it, preferably not in the last slot. I know my park went down to 4 ½ again, but as long as the panda isn't in the last slot and already loading when that happens, you should be fine.
Just a note once you get the pandas... Haha, at first I thought the goal was just to get one, so I was a bit disappointed when I realized I had to breed them. Keep in mind that pandas don't always get pregnant at the 1st try, so you don't get evil surprises like I did
Mine got pregnant at the 3rd try I think. I actually bought a 2nd female in the hopes he'd reach one of them faster, but in the end he bred with the one you got for "free"