tl;dr: Conduct research with 5 users to get the best value for your time and investment. Getting insights from at least 5 users will typically help you uncover the most important issues to resolve.
What is the recommended number of participants for user testing exercises?
For usability tests, 5 users seems to be the magic number. These 5 users will usually point out the majority of your key usability issues. After your first few tests, you'll usually identify fewer issues with each new test.
According to Jakob Nielsen, “With 5 users, you almost always get close to user testing's maximum benefit-cost ratio.”
This means that you'll receive the most important usability findings from 5 users, and testing with additional users is not as critical. You'd potentially be better off stopping at 5 users, making adjustments to your prototype or design, and then returning for a new batch of interviews.
What is the recommended number of participants for user interviews and market research?
Broader user interviews and market research sessions are slightly different and there are multiple variables that affect the ideal number here. Starting with 5 users is still a sensible choice, but be prepared to conduct further research with additional people, potentially as many as 8-15 different users, and sometimes 30 or more.
Unlike user testing, where the number of interface issues that can be uncovered in a 1 hour interview is potentially finite, you can absolutely learn and understand more about a market problem by including extra users in market research sessions. This is especially so if you're researching a complex problem.
If you have multiple personas, you'll also probably need to multiply the number of sessions required, by the number of personas you're researching.
To get started, scheduling interviews with 5 initial users should give you a pretty good understanding of people's feelings on your research topic. After those 5 interviews, you should be able to make a good judgement of whether it would be valuable to interview more people and get additional perspectives.