192.168.1.5
69.52.220.44
10.152.16.23
192.168.3.10
192.168.1.4
192.168.2.1

10.152.16.23
69.52.220.44
192.168.1.4
192.168.1.5
192.168.2.1

var unsortedIps =
    new[]
    {
        "192.168.1.4",
        "192.168.1.5",
        "192.168.2.1",
        "10.152.16.23",
        "69.52.220.44"
    };

var sortedIps = unsortedIps
    .Select(Version.Parse)
    .OrderBy(arg => arg)
    .Select(arg => arg.ToString())
    .ToList();

69.52.220.44 =>

69 * 255 * 255 * 255 +
52 * 255 * 255 +
220 * 255 +
44