getting records in invalidemployeenumber list

I think the issue lies in the regular expression used to validate the employee ID. The regex pattern @"^[0-9]{5}$" matches exactly 5 digits. However, you mentioned that the employee ID can have a length between 4 and 14. Try this once:

string numericRegex = @"^\d{4,14}$";

Put(SurveyRecipientViewList _SurveyRecipientViewList)
{
    if (!ModelState.IsValid)
    {
        // Handle invalid model state
    }

    ClaimsPrincipal principal = Request.GetRequestContext().Principal as ClaimsPrincipal;
    Int32 LogedInID = Convert.ToInt32(principal.Claims.FirstOrDefault(t => t.Type == "LogedInID").Value);

    var result = from c in db.Contacts
                 join cm in db.ContactEmails on c.ContactID equals cm.ContactID
                 select new SurveyRecipientView
                 {
                     EmployeeID = c.EmployeeNumber,
                     FirstName = c.FirstName,
                     LastName = c.LastName,
                     EmailAddress = cm.EmailAddress
                 };

    List axe = result.ToList();

    ValidateRecipientList _ValidateRecipientList = new ValidateRecipientList();

    try
    {
        string strRegex = @"^(?("")("".+?(? new { grp.EmailAddress, grp.EmployeeID, grp.FirstName, grp.LastName })
            .Where(g => g.Count() > 1)
            .Select(grp => grp.FirstOrDefault())
            .ToList();

        _ValidateRecipientList.DistinctRecords = _SurveyRecipientViewList.SurveyRecipientView
            .GroupBy(grp => new { grp.EmailAddress, grp.EmployeeID, grp.FirstName, grp.LastName })
            .Select(grp => grp.FirstOrDefault())
            .ToList();

        _ValidateRecipientList.InvalidEmailAddress = _ValidateRecipientList.DistinctRecords
            .Where(t => !EmailRegEx.IsMatch(t.EmailAddress))
            .ToList();
        _ValidateRecipientList.DistinctRecords = _ValidateRecipientList.DistinctRecords
            .Except(_ValidateRecipientList.InvalidEmailAddress)
            .ToList();

        _ValidateRecipientList.InvalidEmployeeNo = _ValidateRecipientList.DistinctRecords
            .Where(t => !NumericRegEx.IsMatch(t.EmployeeID.Trim() == "" ? "00000" : t.EmployeeID))
            .ToList();
        _ValidateRecipientList.DistinctRecords = _ValidateRecipientList.DistinctRecords
            .Except(_ValidateRecipientList.InvalidEmployeeNo)
            .ToList();

        // Rest of your code goes here...

    }
    catch (Exception ex)
    {
        // Handle exceptions
    }
}