The premises are (actually) false but we can imagine that they are true while still claiming that the conclusion is false. No invalid argument is sound.

Consider:

The president of the United States must be 35 years of age or older.
Baby Elizabeth, born 30 days ago, must be 35 years of age or older.
So, Baby Elizabeth, born 30 days ago, is president of the United States.

If Baby Elizabeth, born 30 days ago, is president of the United States, then Baby Elizabeth, born 30 days ago, must be 35 years of age or older.
Baby Elizabeth, born 30 days ago, must be 35 years of age or older.
So, Baby Elizabeth, born 30 days ago, is president of the United States.

For either example, the logic is invalid and the premises are false. For the premises to be true, all of them need to be true. But, for the premises to be false, only one need be false. So, an argument with a mixture of true and false premises is still considered to be an argument with false premises--it is false that all of the premises are true. Nevertheless, in these examples, the conclusion is false.

For either example, the logic is invalid and the premises are false. Here the conclusion is false. Invalidity is a no guarantee of a false conclusion when the premises are false. False 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.