Is zakat obligatory on a piece of land registered in the name of a person who did not desire it, and his mother managed it through a power of attorney from him, for the past five years?

Your mother is obligated to pay Zakat (definition) on the land if she purchased it with the intention of trade, or with the intention of trade combined with the intention of ownership if she intended to sell it upon making a profit. This Zakat would be for the period the land remained in her possession before she gifted it to you and your brother. However, if she did not intend trade at the time of purchase, then neither she nor you owe any Zakat on it.