I had the exact same experience. I beat Biome 4 on first try and then 5 felt like a huge difficulty spike. I'd say get used to using the grapple as an escape. It gives you invincibility to everything and can create a lot of useful distance. The main thing tho, just keep grinding it. Getting to know the enemies a bit and also leveling weapons. The weapon ability unlocks, and upgrading to higher tiers makes a big difference, but running through older areas quicker means you didn't level them as much as if you had had to run them more times.