CreateCustomAestTimezone.cs

// https://docs.microsoft.com/en-us/dotnet/api/system.timezoneinfo.createcustomtimezone?view=netframework-4.7.2
void Main()
{
	TimeZoneInfo
		.ConvertTime(
			DateTimeOffset.Parse("2019-02-18 19:51 -05:00", CultureInfo.InvariantCulture),
			TimeZoneInfo.FindSystemTimeZoneById("AUS Eastern Standard Time")).Dump("Sydney Time");
	TimeZoneInfo
		.ConvertTime(
			DateTimeOffset.Parse("2019-02-18 19:51 -05:00", CultureInfo.InvariantCulture),
			CreateAusEastTimezone()).Dump("Sydney Time");
}

// Define other methods and classes here
private static TimeZoneInfo CreateAusEastTimezone()
{
	TimeZoneInfo.TransitionTime startTransition, endTransition;
	startTransition = TimeZoneInfo.TransitionTime.CreateFloatingDateRule(new DateTime(1, 1, 1, 2, 0, 0),
																	  10, 1, DayOfWeek.Sunday);
	endTransition = TimeZoneInfo.TransitionTime.CreateFloatingDateRule(new DateTime(1, 1, 1, 2, 0, 0),
																	4, 1, DayOfWeek.Sunday);
	var adjustmentRule = TimeZoneInfo.AdjustmentRule.CreateAdjustmentRule(
		DateTime.MinValue.Date, 
		DateTime.MaxValue.Date, 
		TimeSpan.FromHours(1),
		startTransition,
		endTransition); 
	return TimeZoneInfo.CreateCustomTimeZone(
		"AU Eastern Standard Time",
		TimeSpan.FromHours(10), 
		"AEST", 
		"AU Eastern Standard Time",
		"AU Eastern Daylight Saving Time",
		new[] {adjustmentRule});	
}