Brain-Teaser 731: A little list

From The Sunday Times, 20th July 1975 [link]

(1) In this list there is a true statement and a false statement whose numbers add up to give the number of a false statement.

(2) Either statement 4 is false or there are three  consecutive true statements.

(3) The number of the last false statement subtracted from the product of the numbers of the first and last true statements gives the number of a statement which is false.

(4) The number of even-numbered true statements equals the number of false statements.

(5) One of the first and last statements is true and the other is false.

(6) When I first sent this problem to the editor, thanks to a typing error no sixth statement was included. However the answer to the following question was the same then as it is now:

Which statements are false?

This puzzle was included in the book The Sunday Times Book of Brain-Teasers: Book 2 (1981, edited by Victor Bryant and Ronald Postill). The puzzle text above is taken from the book.