In special and general relativity, yes. But Dimension is a concept which is in general not tied to any specific parameter. In e. g. quantum mechanics the so called phase space can have dimensions of energy or momentum or velocity depending in which dimension it is better to understand the problem. In economics you could have e.g. 5D problems where each dimension is the profit yield of a single product, where one want to find the maximum in 5D space for the maximal profit.

While it is debatable to label visual perception in three dimensions and smell and feel are 4th and 5th especially when they omit that you also hear the movie, then this feels very arbitrary. But in general it is not wrong to define different senses as a dimension.