This is for 5e, I need an explanation of progression, skills, and stats, and how they all work. This might be a heavy question, so if there's a simple book that explains this stuff, I'd like to know what it is. It probably does exist, and I'm irresponsible for not locating it, but I guess that's my question. If there's a book/website/etc. that teaches me how to play the game in terms of character progression, skills, stats, magic, weapons, items, all of that. I'm extremely new to D&D and I'd love to learn the game to play with my friends.
The Player's Handbook is the book that has all of the core rules and player character options. However, there are other options if you're overwhelmed or have limited cash.
Basic Rules is an official supplement that has the basic rules and content of the game. These are a sample of the rules you can find in the Player's Handbook
5th Edition SRD is an unofficial wiki that has many of the content and rules found in the Player's Handbook.
Starter Set is a product specifically designed to introduce new players to the game and tabletop roleplaying games in general.
Player's Handbook is the official rulebook for the game and has all of the core content of the game.
Dungeon Master's Guide is the official rulebook for running a campaign and teaches you how to be the Dungeon Master (the player responsible for creating adventures).
To learn the basics, a great place to start is the D&D Starter Set. It not only covers the basic rules, but has pre-generated characters and an adventure that will bring them from level 1 to level 5.
If you don't want to spend the $20, you could also go with the D&D Basic Rules which are free to download:
Once you've gotten comfortable with these, then you could make the investment to get the Player's Handbook.