How often do you want your 5 cycles? Do you want the cycles to be switched on at a certain part of the waveform. It looks like pin 3 controls the output level, so link it to V cc with a high value resistor. Then a 555 timer chip can be used as a monostable, if you set its time to (250KHz = 4 microS period X 5) to 20 microseconds to the output of the 555, then every time you fire the 555, it will short out pin3 and STOP 5 cycles. So you need to put a transistor invertor in the way so the output of the transistor switches on the XR2206. You can fire the 555 from a push button or some other oscillator. This setup is non synchronous so it will switch the 250 KHz anywhere on its wave form.
Frank