Why does my oil furnace cycle quickly?
Yes I would call 5 to 10-minutes with a heat pump is a short cycle. You or someone needs to trouble-shoot to see what is interrupting the signal to the compressor contactor. If it is coming from the thermostat it could be programmed wrong. If you want a non-programmable Heat Pump stat try Honeywell #RTH3100C.  Many companies make this though.  Google non-programmable heat pump thermostat.