How long do sperm live after ejaculation?

That depends on where they are. In the female vagina, the conditions are usually such that the sperm live for 4 to 5 days, so that fertilization can occur. Outside of that, they can only live for a few minutes or an hour, depending on moisture and other variables. Millions of sperm are ejaculated with each climax, so the number of sperm still living will dwindle with time until eventually they all die.