Here are the following requirements to earn a Level 5 Archer Tower:
Level 1 – 200 Wood. A Lumberyard (150 Food) is required to store Lumber. This is part of the tutorial.
Level 2 – 1,600 Wood. A Level 2 Lumberyard will need to be acquired to stockpile the required amount.
Level 3 – 2,750 Wood. A Level 3 Lumberyard will need to be acquired to stockpile the required amount.
Level 4 – 4,500 Stone. A Level 3 Keep (2,750 Wood) is needed to build a Storehouse (2,500 Wood) for stone and a Level 4 Keep (6,000 Wood) is needed to construct a Quarry (4,000 Wood) to generate Stone.
Level 5 – 14,500 Stone. In order to hold at least 14,500 Stone, a Level 2 Storehouse (8,000 Wood) is needed. With a Level 2 Storehouse, a Level 5 Keep (20,000 Wood) is needed to unlock the ability for the final upgrade.
I don't have the number totals for the Lumberyard Lvl 2-3 as I upgraded past them before writing this.