Safari is a 20 minute ride. It can be more if an animal decides to park itself in front of your vehicle for a while. If you are booking a FP+, you might want to do it a little before 4:30 to account for the line to get to the ride and the ride itself. I think you would be okay for a 5:15 Tusker House with a 4:30 FP+ as they are right next to each other, but you might want to try 4:00 or 4:15 to be safe. The FP+ line can be hit or miss on that one, we have had to wait 20 minutes in the FP+ line, and we have walked on. If you are not doing FP+ for it, realize that the standby line around that time will be anywhere from 20 minutes to an hour. I don't think it would be more than an hour that late in an AK day (although it is possible), and it does tend to get a little shorter later in the day, so my best guess would it would be somewhere between 20 and 40 minutes. So, I would not expect to walk up to the standby line at 4:30, get through that line, get through the 20 minute ride and be at Tusker House by 5:15. You definitely want to go earlier if you are going standby to be safe. You don't want to miss Safari at AK!
I would not plan on attempting to ride Safari after Tusker House (unless that is your 2nd ride on Safari for the day), as I think you would be cutting it too close to closing. We eat at TH every trip. They have now added characters at dinner, so I would expect it to be a more popular dinner destination now. Sometimes, there can be quite a wait for your table at TH There have been times when we have gone for breakfast or lunch that we have not been seated until 20 or 30 minutes after our ADR. You might be seated right on time, but in case you are not, you don't want to risk missing Safari, if you don't get out of TH in time. It is not unusual for a meal at TH to take an hour and a half by the time you get seated and have the character rotation get through. If the meal took you an hour and a half, then you would miss getting to the Safari line in time.
I wouldn't worry about which time the animals will be out. I've always heard Safari is best in the morning, but one time we went in the afternoon and it was one of the best times we have gone animal wise. They were all over the place and very active. You just never know what you will get with animals. I would ride it before you go to TH, and then if you get out of TH in time, you can always go over and ride it again.