If the condom does not contain spermicide, how long does the sperm stay alive?

If your question relates to those left in a condom after use, It is likely only hours. Inside the vagina they can survive up to 5 days. If the condom full of sperm is subjected to hot/cold/water or drying they might die quicker.

By babymed.com website: "a sperm sample collected in a sterile container at body temperature may remain alive for several hours, but the sperms' fertilizing capability drops dramatically within 60 minutes after ejaculation". A condom without spermicide may be less ideal than a sterile container so I would assume the sperms will last less than several hours.

As long as the condom doesn't come off, whether spermicide is present or not than no pregnancy will occur. The sperm dies in a few minutes [3-5] in a used condom but can live in the vagina for 4- 5 days. Keep using safe sex procedures and no concerns will occur.