Let me illustrate what I was talking about re: using higher level monsters sooner. I'll use the infamous blue dragon encounter in HotDQ
In 3e, the adult blue has an AC of 28, +27 attack bonus, and an SR of 21. There is no way in hell a 1st level group of players or guards will even hurt the thing outside of a natural 20, and the dragon will always hit unless it rolls a natural 1.
In 5e, the blue has an AC of 19, +12 attack bonus, and no spell resistance. Most 1st level PCs have a +4 through +6 attack bonus, and most guards have a +4. That means they will hit on a 15 or higher. They also have an AC between 15 and 18, meaning the dragon would need more than just a 2 to hit them. And 1st level spells will still be effective.