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.