By definition, every argument with true premises and a false conclusion is INVALID. So is every argument for which we can invent a story in which the premises are true and the conclusion false. Only, in this case, we do NOT have to invent the story--reality is the story.

Consider:

The president of the United States must be 35 years of age or older.
Elizabeth Taylor must be 35 years of age or older.
So, Elizabeth Taylor is president of the United States.

If Elizabeth Taylor is president of the United States, then Elizabeth Taylor must be 35 years of age or older.
Elizabeth Taylor must be 35 years of age or older.
So, Elizabeth Taylor is president of the United States.

For either example, the logic is invalid but the premises are true. Here the conclusion is false. Invalidity is a no guarantee of a true conclusion when the premises are true. True premises can lead to either a true or a false conclusion in an invalid argument. In these examples, bad luck rather than bad logic led to the false conclusion. But, that the premises are true and the conclusion is false conclusively proves that this argument is invalid since they are the defining condition.