Session 5 of the Mindfulness Institute discusses the importance of setting goals while being mindful of potential pitfalls, such as excessive focus on future outcomes leading to decreased attention on the present moment. It emphasizes radical acceptance as a way to cope with reality and highlights the paradox of goal striving possibly leading to negative thoughts and frustration. The session encourages mindfulness to enhance present-moment awareness, reduce fear, and foster gratitude, ultimately improving satisfaction and productivity.