Q.When flowers fall from the stem of an orchid, do I cut off the stem?
I don’t know what kind of orchid I have, but it looks like the moth orchid and had 5 flowers when I bought it for Mother’s Day. Now all 5 flowers have dropped, a new leaf is appearing and I need to know what is the next step? Do I cut the stem the flowers were on?

Generally leave the stem on, because sometimes they sprout new plants or flowers. The most important thing to do with an orchid is to repot it into orchid mix if it's in sphagnum moss, which is the way most commercial orchids are grown today. Here are a couple of articles to help you: https://www.gardeningknowhow.com/ornamental/flowers/orchids/indoor-orchid-care.htm
https://www.gardeningknowhow.com/ornamental/flowers/orchids/repotting-orchid-plants.htm