I agree with Nicholas. You can use a polynomial or ordinal logistic regression. Or else you can change your ordinal 5 or 6-category outcome variable, for example, to a binary variable using any cut-off point like '2' and use a simple logistic regression model.

But Wilcoxon rank sum test would be univariate analysis while one can adjust for different confounders in polynomial or ordinal logistic regression.

You can use a Wilcoxon rank sum test since the dependent variable is at least ordinal but considering this I would choose an ordinal logistic regression because it will give me an easier interpretation of the ordered log-odds coefficient which would be that for a one unit increase in the predictor, the response variable level is expected to change by its respective regression coefficient in the ordered log-odds scale while the other variables in the model are held constant.