Of course, it all depends on what and how you want to shoot.
If I were you, first, I would figure out for my shooting if I'd need 2.8 or if F4 would be enough. You have a new enough DSLR with good high ISO capability, it's something to consider.
Second, if I picked 2.8, for example, you need to figure out how specialized do you want to go for both sports and landscape.
I personally also shoot both of them, and I hate having 5 different lenses, because then it's always tough for me to choose which one to use. In my kit as you can see, I am only using 24-70 and 70-200, giving me the best most used focal lengths, keeping my kit light.
If money was no object, and if I didn't care about having multiple lens, my list would consist of
16-35
24-70
70-200
and whatever I could afford for the long zoom, either 100-400 or 200-400.
For some landscape shots, having the wide end of 16mm from 16-35 might look pretty good. But I have seriously in all my years of shooting very rarely found the absolute need for the 16mm shot. Sometimes I can just take two to three shots from 24mm and stick them in Photoshop, which now is super easy to do. Gives the same result, and costs a lot less. Plus I don't have to have a lens with me in my bag just for the one shot.
Again, same issue with the sports photography. 300-400mm zoom will give you a better closeup on a large stadium if you're sitting far away. But over the years I had good results with the 200mm lens which is RAZOR SHARP, and I am sure combined with Mark IV, which has better res to be able to crop if you need to, you could really get very good results if you just position closer.
It all comes down to your budget and how many lenses you want to carry around with you, some just for the 1 shot. I made a decision of going with the least amount of lenses and I really don't regret it.
EDIT:
I do notice that you're picking up the 100-400 lens for your zoom. I haven't personally shot with it, but I can almost guarantee that 70-200 has better IQ and sharpness. Canon's 70-200 literally has razor sharpness, so even for the mid to long zoom range, I would imagine IQ would probably be better than 100-400 zoom. Just something to consider, I am sure the reason you picked 100-400 is because it lens you keep one lens on during sport events for the longer reach, but that IQ from 70-200 is addictive.