No.
I must've misunderstood you.
What do you want to do?
Do you want it to trigger a 5 second long output pulse if the input pulse lasts for longer than a second? Yes, but the input pulse will NOT be longer than a second.
For this you need two 555s, I can post the circuit if you want.
Do you want to trigger a 5 second long output pulse when the input goes positive? NO I need a delay of 5 seconds after the initial input pulse of 1 second. Then I need a 1 second output pulse.
To do this just connect a small NPN transistor (BC547, 2N2222, BC109 etc.) in series with C2 and a 100K in series with the base which will be the input, you might also want to add 10nF from pin 5 to ground. I'll show you if you don't know how.