Can a job deny you if you had a felony 8 years ago but they only asked if you've had one in the past 5 years?

Deny what? Employment? The answer varies from state to state. You did not identify your state. If you are not in GA, resubmit your question and identify your state. In GA, you may be discharged for "had a felony" or any other reason, so long as that is the real reason, and not a trick to fire you for some illegal reason. In GA, the only illegal reasons are: Race, age, sex, national origin, religion, or handicap. If it is not on that list, it is not protected, and may be a basis for a completely lawful discharge.