using System;

using System.Collections.Generic;

using System.Globalization;

using System.Linq;

public class Program

{

        public class Logs

        {

            public DateTime Date { get; set; }

            public string Name { get; set; }

            public string Activity { get; set; }

        }

        public static void Main(string[] args)

        {

            var UserDateTime_TEXT = @"02/02/2018 02:20    

05/02/2018 15:20    

21/02/2018 12:00    

21/02/2018 13:00    

21/02/2018 15:00  ";  

            var UserActivity_TEXT = @"User logs on

User visits page

User goes here

User logs off

User logs on

User visits here";

            //Equivalent to ReadAllLines

            string[] UserDateTime = UserDateTime_TEXT.Split(new[] { Environment.NewLine }, StringSplitOptions.RemoveEmptyEntries);

            string[] UserActivity = UserActivity_TEXT.Split(new[] { Environment.NewLine }, StringSplitOptions.RemoveEmptyEntries);

            // ps in your exemple there is more activity than date time... 

            // UserDateTime.Length != UserActivity.Length !!!!!!!!!!!           

​

            var data = new List<Logs>();

            //in your code you had `x < UserActivity.Length`, what is x?

            for (int i = 0; i < UserDateTime.Length; i++)

            {

                var splitValues =  UserActivity[i].Split(' ');

                var temp =

                        new Logs

                        {

                            Date = DateTime.ParseExact(UserDateTime[i].Trim(), "dd/MM/yyyy HH:mm", CultureInfo.InvariantCulture),

                            Name = splitValues[0], // No space in username. 

                            Activity = string.Join(" ", splitValues.Skip(1))

                        };

                    data.Add(temp);         

            }

            data.Dump();

            //filter

            var greaterThanThis = new DateTime(2018, 2, 20);

            var result = data.Where(x=> x.Date > greaterThanThis);

            result.Dump();

        }

}

​