The depended variable is Binary data and independent variables are ranks from 1 to 5.

I suppose that you have more than 1 independent variable?

For binary dependent variables a binary logistic regression

could be used. Predictors which are ranks should be transformed

into binary variables (4 dummy-variables, one for each rank,

except for one rank which serves as reference) .

If you just want to check bivariate relationships, then you can

use the Mann-hitney U-test with your binary dependent variable

as grouping variable.

With kind regards

K.