But also there nearly the same problem: 220Hz doesn’t pass but a frequency of 306Hz?!
Probably, your sampling rate isn't defined at 5 kHz, but vary above the spec.
Do you have a scope? If not, i could suggest to use your PC as a freq. meter, set one digital pin as output, and drive it high/low in the loop. Than using audacity or something else, use PC sound card to measure freq. Don't forget to attenuate a voltage from the pin with resistive divider, and put a DC blocking cap