Floating Supply Outputs
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Can you post your transformer winding order and primary and leakage inductance values. Also post what your layout looks like. Generally these problems occur if there is loose coupling between the regulated output (5 V) and the unregulated output (15 V). This may also happen if the loop area for the 15 V output is large.
attaching a few things about your layout. The loop areas on the secondaries need to be small. Length of traces which carry switching currents and voltages should be small. The location of feedback resistors should be moved to the right near the output. This will make room to move switching components closer together.
See some of the multiple output layouts from PI (RDR-115)
http://www.powerint.com/sites/default/files/PDFFiles/rdr115.pdf
What you have is the classic cross-regulation problem. By how much is the 15 V output dropping? What kind of tolerance are you expecting on this output? If you want to drive a MOSFET you probably need only 10 to 12 V
I can suggest a couple of things you can try
1) In the transformer construction place the 15 V winding immediately next to the 5 V winding. This improves coupling between the 5 and 15 V windings
2) Try to minimize the secondary trace inductances for this 15 V output (Place its diode as close to the transformer bobbin pin as possible)
Let me know what voltage you are seeing on 15 V when loaded...