The short answer is yes. I constructed similar models where I sought to predict a conditional outcome based a some discrete inputs similar to yours. One method is the use, in your case four, "dummy variables" where you assign a binary response in the model given the questionnaire answer. Assume the questionnaire answer "1" is the base case, hence the use of only four independent dummy variables in the model. You can also just use the questionnaire response in the model, but his can be problematic hence the use of dummy variable. One final method based on what you are trying to model is to assign a new binary outcome based on a responses in the questionnaire, for example responses 1 -3 would equate to an outcome of "1", while response 4 and 5 would be coded as a "0" outcome. I have attached an article detailing this process for your reference.

The long answer is no if your likert data is for a DV. In that case you need ordinal logistic regression because LIKERT DATA IS ORDINAL and cannot be approximated by anything else. There are litterally tons of these questions in this section. Again IF THE DV IS LIKERT THEN USE ORDINAL LOGISTIC REGRESSION. For a start into the lit you might begin here:

My tome on Likert DV’s and ordinal logistic regression can be found here:

https://www.researchgate.net/post/Can_you_help_with_statistical_analysis_advice

https://statisticalanalysisconsulting.com/how-to-analyze-likert-type-dependent-variables/

https://www.researchgate.net/post/Possibility_of_using_point-scale_data_in_a_mixed-model_ANOVA

There are many others. I suggest you search these questions looking at David Morgan's replies as well.

Best, D. Booth

PS I have attached some notes that may be helpful.

Yes, it is possible to make a prediction of the probability of the event occurring using logistic regression