Don't use a regex: you can do it, but it's horribly complex when you start thinking about 28 day months, 30 day, and 31 day months, and then there are leap years...
Try:
DateTime dt;
if (DateTime.TryParseExact("04/17/2015", "MM/dd/yyyy", CultureInfo("en-US"), DateTimeStyles.None, out dt))
{
...