5th edition gives loads more room for the DM than in 4th edition. All you have to do is go back and compare the 4th edition PHB to the 5th edition one and you will see which gives more options and which gives more freedom to players and DM's.
I'm pretty familiar, and you're just confused over what 'more options' and 'more freedom' means.
The GM in any RPG can change the rules, add to them, or toss them out. That's an innate freedom that every GM has in every system. Some games, like 5e and Storyteller (and, ironically, 3e) come right out and tell you that you have this freedom. And some feel that doing so absolves such games from providing complete, playable, or even functional rules - going so far as to opine that rules are all just a red herring, anyway, and that the OneTrueWay is essentially Freestyle RP. Happily I haven't seen anyone trying to drag 5e down that particular rabbithole, yet. But, Storyteller sure got more than it's fair share of that when it was big.
So, the DM always has total freedom, whether the game provides him with many rules or few, and whether those rules are good or bad.
So, yes, the DM has absolute freedom in 5e, and it's nice that 5e hammers that point so relentlessly, because it makes it less likely that players will rebel against the idea like they did in 3.x/Pathfinder with the community-wide RAW-obsession.
And, I do like that about 5e, but it's as far as it goes in 'empowering' the DM. As a DM, I have the same power in any system. It's a matter of attitude. It's 'soft support.' I really shouldn't be trying to explain this to you, afterall, you might be a player at my table some day, and the last thing I'd want to do is dissuade you of the impression that I'm uniquely empowered as a 5e DM and you don't dare challenge any of my rulings. (I'm an experienced DM, my rulings are pretty good, anyway).
4th edition is too heavily relied on the powers and staying with in the confines of those powers. Can you change anything? Sure you can, you can do that in any edition of D&D it's just that 5th edition gives more power for that sort of thing.
There's no such thing as 'more power,' when you already have absolute power.
Options, OTOH, can be seen differently. 5e presents the players with some options: 12 classes and 38 sub-classes. The Warlord, Psion, Avenger, Psychic Warrior, Scout, Shaman, Beguiler, Battlemind, and many others from other editions are not among those classes. All those 5e classes can cast spells, and the 5 sub-classes that eschew any sort of spell or magical abilities are all unalterably specialized in DPR in combat.
So there are some options you don't have in 5e, as a player. You can't play a 'martial' character with a speciality other than DPR, like a Warlord. You can't play a psionic (yet). Etc The DM could always add to that list of options, but you as the player lack both options and freedom.
The DM, OTOH, in addition to his inevitable absolute freedom, is presented with a fair number of options. The DMG is full of optional rules, and even the PH has rules that the DM must decide to 'opt into.'
5e is very much a DM's game. That 'DM empowerment' is real, in a sense, even though the DM's 'power' to change a system he is running is absolute, regardless of system. Perhaps the dis-empowerment of players is the more significant factor. The DM's absolute freedom to change/mod/add-to the game is made more evident by the Players' constricted options and absolute lack of such freedom.