Hey there! I have not used this, sorry.
First, don't take this if you're on medication targeting serotonin receptors, such as an ssri or snri. Assuming you're not on medication, the answer is, maybe, maybe not. The same answer you'd get if you went on medication. Sometimes things work, sometimes they don't. Second, 5-HTP isn't a vitamin -- it's an amino acid, a metabolite of L-tryptophan, which along with co-factors such as B6 (which is a vitamin) us used by the body to manufacture serotonin. If you metabolize it well and that's what your body thinks you need, then it might help. But if your problem is confined to public speaking anxiety, the most common kind, and it's not a generalized problem, I'd probably start by seeing a therapist or other professional who specializes in treating this problem, or maybe taking a public speaking course and practicing until you lose your fear of it. Or learning some CBT type techniques of relaxation and demystifying the situation. There are herbs and other amino acids, such as taurine, that can also be helpful, though any relaxation supplement or medication can cause sedation. 5-HTP would normally be used for more chronic and generalized forms of anxiety and depression, but again, only trying it will tell you if it will help.