Try this:

Without sampling a large population of your nvarchar date data, I will assume the example you gave will be sufficient.

Here I simulate your scenario.

declare @TestDateValue nvarchar(50)

set @TestDateValue = '01/01/05'

select cast(@TestDateValue as datetime) as NewTestDateTime

The variable @TestDateValue is now a datetime. If milliseconds are not necessary, you could also use:

select cast(@TestDateValue as smalldatetime) as NewTestDateTime

I hope this helps.

-Mike