A five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in N-dimensional space. If interpreted physically, it is one more dimension than the three usual spatial dimensions and the fourth dimension of time used in relativity physics. In 1905, Albert Einstein demonstrated in his Special Theory of Relativity that space is intimately connected to time through the cosmic speed limit of light, so, strictly speaking, we live in a universe with four dimensions of space-time.
However, for everyday purposes, we think of the Universe in three dimensions of space (north-south, east-west, up-down) and one dimension of time (past-future). In that case, a fifth dimension would be an additional dimension of space.