It may depend on the insurance company, but many insurer offer term life insurance plans to people up to age 75.
For example, a 75 year old may be able to purchase a 5 or 10 year term life plan, depending on his or her health.
Whereas, a 15 year term life policy may be available to people up to age 65 or 70.
After age 75 it may be difficult to get approved for a term life insurance policy.
Learn more about age limits on term life insurance policies.