Best clustering algorithm to identify clusters and determine the closet cluster each individual response is near? I have a survey where each question is related to a different 'shopper' type (there are 5 types so 5 questions). Each question is either binary (True/False) or scale based.

IE:

1. Do you like to shop at our physical location store ? (True/False)

2. Do our discounts entice you to shop more? a. no b. maybe c. yes


For each response I convert the answer choice to a numerical value. So True becomes 1, answer choice 2C becomes 3 etc. 

At this point, I am clueless as too what clustering algorithm to use so I can create clusters for each of the 'shopper' types and measures each individual survey response submitted to determine a single cluster closet to the responses given and label the response as that cluster.

IE. This individual that submitted the survey response is 'location conscience shopper type'

Open to any new method of analysis not just clustering
Since they are categorical variables, I would cluster them using the k-medoids clustering method. Before applying this method, one-hot encode all the predictors.

See a tutorial here:
https://towardsdatascience.com/k-medoids-clustering-on-iris-data-set-1931bf781e05

Sklearn has an implementation:
https://scikit-learn-extra.readthedocs.io/en/latest/generated/sklearn_extra.cluster.KMedoids.html