Is there any known reason the two books are identical in topic, except that in 5th edition drakes are not at all in the book?
Since most of what I have to say here is based on in person and online discussions with Catalyst Devs and Writers, you can only take this as second-hand info that I remember. I've heard discussions on message boards and talked with devs at GenCon when I could. So, again, I have nothing written down or concrete to prove this.
Dragons have, since they were first introduced to Shadowrun, been on the top of the food chain when it comes to native Earth creatures. There are other beings, such as spirits and horrors in the story-line of the SR and Earthdawn universe that make the Great Dragons worried, but as far as normal mortal creatures are concerned...oh my god, dragons.
Both in the literature and the core rule books, dragons have been put on a pedestal that not many people can knock them off of. It takes a concentrated effort to even damage a dragon, let alone kill one. And we're talking about normal dragons here. We're not even talking about Great Dragons, like Lofwyr or Hestaby. We're talking about the dragons that you will rarely see in a game. Your options, when a dragon is actually angry at you, is running as fast as you can, as far as you can, shooting the biggest guns you have, and hoping that the dragon just gets tired of chasing you and goes off to do something else.
Dragons are scary. Great Dragons are terrifying in what they can do to you. And not just you, but entire armies. In Storm Front, at least two Great Dragons were assaulted by large armies. And only one of those Great Dragons were confirmed dead. And this is after we developed weapons to act as poison to dragons and dragon kind, just so we could kill the sons of bitches. They have massive power, are massively strong, and have eternal patience. They are immortal and will simply wait you out, because your small mortal life is the blink of an eye to them. Hell, they have (rules as written) powers to straight-up nullify an edge roll of yours. They can tell fate 'No', and fate listens.
All of this goes to the point that I want to make. Drakes were pulled out of character creation because they were way too out-there to have as a PC race. While a drake is only a fraction of what a dragon could be, it's still insanely powerful and ruins their mystique of what a dragon is. If everyone can walk around being a Jedi, Jedi's would stop being cool. If everyone walks around as a drake, dragons stop having that 'out of our league' feeling you want to give to a player.
Plus, you shouldn't be dealing with a dragon anyways. ;)
(Please note that this information is through second-hand sources and I have no real vetting process for it. I have tried to write this post without blatant copying or mimicking of other opinions and thoughts.)
5ed books aren't direct upgrades from 4ed books; they have so far diverted from the previous and touched new subjects, while scratching stuff previously mentioned in the rules (like spell formula creation). In this case, Drakes and Free Spirits were left out.
Keep in mind though that even when a bunch of spells were left out of Street Grimoire, they appeared later in Shadow Spells (PDF-only supplement). So there is a chance we will see Drakes and Free Spirits in a future supplement as well.
As for a reason, I believe they don't have a strong one other than try to avoid drake PCs and keep those for NPCs instead, for the same reason we are not allowed to play true dragons or other sentient metacritters.
But if you really wish to play one, you can easily convert the 4ed player companion rules to 5ed: attributes changed very little, critter powers have all been converted to 5ed already, you just need to assign a race priority and special points (if any).
As an update to this old question: Drakes now exist again. Their full rules are now available for shadowrun 5 in the book: Shadowrun Howling Shadows.
It seems to be that either the producers wanted to dismiss drakes and bowed now to popular demand OR they wanted to not put drakes into the compendium but in the more fitting critters book this time around.
About the book itself: This book details critters and also has full rules for drakes and how to create them as PCs and NPCs. The rules are based on using the option to use karma to create characters and are more flexible than the original rules. This time around you got some basic powers and can buy additional ones for a specific amount of karma each.
There are also rules for how long it takes after "awakening" until you can learn each of the additional powers.
Some of them were indicated in the old fluff that drake could get them and some like attaining a partial form are completely new.