First, draw schematics properly when you ask others to look at them. Your right to left flow is rather annoying.
There are two main possibilities for this circuit to cause noise, the inductor and the output capacitor.
The inductor can make sound for two reasons:
- Every bit of wire is subjected to a sideways force due to the magnetic field. As that changes, the force on the wire changes. The windings aren't meant to move, but small vibrations happen anyway.
- The magnetorestrictive effect. Some magnetic materials change size slightly as a function of the magnetic field.
The capacitor can make sound due to the piezoelectric effect. This is the electrical analog of the magnetorestrictive effect. The material changes size slightly as a function of the electric field.
The reverse is also true, meaning the voltage on a ceramic capacitor can change slightly due to applied force. This undesirable property even has a name, called microphonics. This is why ceramic capacitors are usually banned from the signal path of sensitive audio circuits.
4.7 µF for the output cap seems rather small. I didn't read the whole datasheet, but the examples I saw used 10 µF. Maybe it's within specs, but there is certainly no harm in making it higher. That would make the output voltage smoother, which includes less voltage change across the capacitor.
The above explains why this circuit could make sound at the switching frequency. Since that's 1.2 MHz according to the datasheet, that's clearly not what you're hearing. This is actually a symptom of a worse problem, which is that the controller is not stable.
What is happening is that the controller is going meta-stable. Over a number of pulses, the voltage goes up. This causes the PWM to get cranked back for a number of pulses. The result is oscillation at a lower frequency than the switching frequency. This is what you are hearing. You really should fix that.
I'd try paralleling another capacitor across C1. You don't give any specs on C1, so we don't know the voltage rating. For some ceramic caps, the capacitance drops off significantly with voltage. If this is a 30 V cap, for example, then the capacitance may be significantly less than 4.7 µF at 25 V.
I see now that there is a table on page 12 of the datasheet, which says 4.7 µF is sufficient above 16 V output. That doesn't mean that higher values are bad.
Even though the datasheet only says the chip needs 1 µF input capacitance, there is clearly no reason you can't use more. Surely this part works with a 0 impedance voltage source as input. I'd put 10 µF there since that's cheap and easy.
Voltage step-up ratio
You are asking for a voltage step-up ratio of (25 V)/(5 V) = 5. That requires a nominal PWM duty cycle of 80%. That's close to the maximum duty cycle of 85% this chip is intended for.
At these voltages and currents, you really should be using a Schottky diode. They have half the forward drop, and are very fast. I didn't look up your diode, but another possible problem is that it has too long of a reverse recovery time. At over 1 MHz switching speed, this is very important. Any ordinary diode is far from good enough here.
You may still be in spec, but right at the edge pushing some of the limits. Use a little intuition and try to make it as easy for the chip as possible. Like with most things in life, trying to slide by with the bare minimum gets you in trouble eventually when everything else isn't just right.
Using a bigger input cap is a no-brainer.
Using a Schottky diode is a no-brainer, and in fact the lack thereof may well be causing significant trouble.
Most likely a larger output cap would help. The meta-oscillations are due to control instability. The most likely cause of that is insufficient output capacitance. Your "4.7 µF" cap probably isn't 4.7 µF at 25 V.