Create a 4 pieces of Fortify Alchemy Equipment (hat, gloves, necklace, ring)
With the clothing on, create some (4) Fortify Enchanting Potions
Create a new, stronger set of Fortify Alchemy Clothing by drinking those potions.
With the Stronger Set, Create some new Fortify Enchanting Potions (they're stronger as the previous ones.)
Now you'll create your Final set of Fortify Achemy Equipment (hat, gloves, necklace, ring) under influence of those stronger potions.
You now can use this Fortify Achemy set to create as many Fortify Enchanting Potions as you need to improve your other stuff.
Is it possible to get this effect without having 5/5 enchanting? What if you just make more potion rounds? Like instead of 3 alchemy clothing, you make even more?