LINQ group by enum and map to another enum

Dear Experts:
I need to group a list of customers (List<Customer>) where Customer contains this enum

public enum CustomerType
{
  type1,
  type2,
  type3,
  type4,
  type5
}

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to a new enum

public enum NewCustomerType
{
  newtype1,  //map to type1
  newtype2,  //map to type2 and 3
  newtype3,  //map to type4 and 5 
}

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Note: My initial code to map to the first enum:
var sortedDetails = _customers.GroupBy(x => x.CustomerType).ToDictionary(t => t.Key, t => t.ToList());
Your answer should return a dictionary mapped to the new enum.

Thanks