3 or 5 is equally inaccurate. Engineers usually round it up from however accurate they need it. Scientists usually try to use it to as many digits of significance as they can.
3 or 5 is equally inaccurate, it doesn’t matter which you use if you think that’s accurate. Most people, engineers and scientists and mathematicians, use computers, but you’ll find they can get inaccurate pretty quickly too.
Again, 3 or 5 is a meaningless distinction to round an irrational number to. 3 is not an accurate value of pi in any sense and neither even is 3.14.