Let me preface this by saying that I may be wrong in my opinions.
With that being said, I think the best way to explain the ranking system is to respond of the common questions and criticisms of it.
"We should have a permanent ranking system like Halo 3!"
Firstly, this is mostly a matter of opinion, I am just going to explain why in my opinion I think a season based system is better than a static system. I believe that in a world where people want fast, real time information at the blink of an eye, seasonal rankings are the only way to go. With a static ranking such as the 1-50 system employed in Halo 3, at some point you will have played so many games it will be almost impossible to level up due to the tiny change one win would have in the face of the large amount of games previously played. Think of it like this: if you have a 1.0 K/D ratio, it would be much easier to change that ratio with one kill if your total kills were only in the hundreds. If you had thousands of kills, however, It would have very little effect overall. Seasonal rankings, however, allow for one to say “wow I have done really terrible lately, It’s a good thing I will be able to start fresh next month!” This is why I think it is a good idea. I can understand the frustration of having a hard earned rank being stripped from you, but I think you will appreciate it when you have a bad month.
"I won most of my games, why am I only Silver/Gold/Plat?"
This, I believe, is the most misunderstood part of the ranking system. 343 needs to do a better job of explaining this. Here is my analogy: Say you are in your first placement game in FFA. You do very well, winning by a margin of 5. You feel confident going into your next game, and do decently well, but only finish 2nd. The next game you are completely dominated by everyone in the game. Why does this happen? The ranking system works by “trying you out” against other players of various levels. So in the first game you may have played a random mix of players. When you do well the game thinks “Hmm well lets try him out against potential Gold players,” after you do well in match, that the game thinks you might be suitable for diamond, but once you get beaten, the game matches you against other players who have similar skill. Even before you have been placed, the game is pitting you against opponents of similar skill and trying you out at different skills to determine your real CSR. If you post average numbers at a potential Platinum level, you will be ranked platinum, regardless of wins or losses.
"All players should have to start low and grind their way to Onyx/Champs!"
No. Logic wins in this regard. Lets say Snip3down plays his first match of FFA. He wins by a margin of 15 kills. The game will think “wow he was a lot better than the silver players we tried him at, lets try him out at diamond.” Lets say he continues to dominate all his matches even as the game tries him out at Platinum, Diamond, and Onyx. By his last two games he has not dropped a single game. His 8th game consists of players who are either already Champs, or are (like Snip3down) proving themselves to be worthy of Champs. He barely wins his 8th match so the game tries him out at the same level again, this time he gets 2nd place. This proves to the game he belongs in Champs. Why then would he be placed in Diamond or Onyx? If you prove yourself in a certain tier. you will be placed in that tier.
This, my friends, is my explanation of the ranking system in Halo 5. I am no expert, but I feel like a have a firm grasp of the system. Please feel free to discuss as you will.