gistfile1.txt

using System;
using Newtonsoft.Json;

public class Item
{
    public string Name { get; set; }
    
    public DateTime Date { get; set; }
}

class Test
{
    static void Main()
    {
        JsonConvert.DefaultSettings = () => new JsonSerializerSettings
        {
            DateFormatString = "dd'/'MM'/'yyyy' 'HH':'mm"
        };
        
        string json = @"
        {
            'Name': 'Test',
            'Date': '13/02/2019 05:13'
        }".Replace('\'', '"');
        
        var item = JsonConvert.DeserializeObject<Item>(json);
        Console.WriteLine(item.Name);
        Console.WriteLine(item.Date);
    }
}