Table 3.4. Filter coefficients for a 5th order high-pass Butterworth filter

Refer here for an explanation and examples.
 

f8000
f16000
f/fs
b0
b1
b2
b3
b4
b5
a1
a2
a3
a4
a5
45 90 0.005625 0.9444 -4.7221 9.4441 -9.4441 4.7221 -0.9444 -4.8856 9.549 -9.3331 4.5616 -0.8919
55 110 0.006875 0.9325 -4.6624 9.3249 -9.3249 4.6624 -0.9325 -4.8602 9.4506 -9.19 4.4692 -0.8695
65 130 0.008125 0.9207 -4.6035 9.2071 -9.2071 4.6035 -0.9207 -4.8348 9.3528 -9.0488 4.3785 -0.8477
75 150 0.009375 0.9091 -4.5454 9.0908 -9.0908 4.5454 -0.9091 -4.8094 9.2556 -8.9094 4.2896 -0.8264
85 170 0.010625 0.8976 -4.4879 8.9759 -8.9759 4.4879 -0.8976 -4.784 9.1591 -8.7718 4.2024 -0.8057
95 190 0.011875 0.8862 -4.4312 8.8625 -8.8625 4.4312 -0.8862 -4.7586 9.0631 -8.6359 4.1168 -0.7854
110 220 0.01375 0.8695 -4.3475 8.695 -8.695 4.3475 -0.8695 -4.7204 8.9205 -8.4355 3.9915 -0.756
130 260 0.01625 0.8476 -4.2382 8.4765 -8.4765 4.2382 -0.8476 -4.6696 8.7324 -8.1742 3.8299 -0.7185
150 300 0.01875 0.8263 -4.1317 8.2633 -8.2633 4.1317 -0.8263 -4.6188 8.5469 -7.9197 3.6744 -0.6828
170 340 0.02125 0.8055 -4.0277 8.0555 -8.0555 4.0277 -0.8055 -4.568 8.3639 -7.6718 3.5248 -0.6489
190 380 0.02375 0.7853 -3.9263 7.8527 -7.8527 3.9263 -0.7853 -4.5172 8.1834 -7.4304 3.3809 -0.6166
225 450 0.028125 0.751 -3.7548 7.5097 -7.5097 3.7548 -0.751 -4.4284 7.8734 -7.0231 3.1422 -0.564
275 550 0.034375 0.7045 -3.5223 7.0447 -7.0447 3.5223 -0.7045 -4.3015 7.4436 -6.4736 2.828 -0.4963
325 650 0.040625 0.6607 -3.3037 6.6073 -6.6073 3.3037 -0.6607 -4.1746 7.0289 -5.9602 2.5432 -0.4366
375 750 0.046875 0.6196 -3.098 6.1959 -6.1959 3.098 -0.6196 -4.0479 6.6292 -5.481 2.285 -0.3839
425 850 0.053125 0.5809 -2.9044 5.8088 -5.8088 2.9044 -0.5809 -3.9212 6.2442 -5.0341 2.0511 -0.3374
475 950 0.059375 0.5444 -2.7222 5.4443 -5.4443 2.7222 -0.5444 -3.7947 5.8737 -4.6178 1.8393 -0.2964
550 1100 0.06875 0.4937 -2.4687 4.9373 -4.9373 2.4687 -0.4937 -3.6051 5.3448 -4.0468 1.5589 -0.2438
650 1300 0.08125 0.4329 -2.1643 4.3286 -4.3286 2.1643 -0.4329 -3.3528 4.6886 -3.3772 1.2455 -0.1874
750 1500 0.09375 0.3788 -1.8942 3.7885 -3.7885 1.8942 -0.3788 -3.1011 4.0869 -2.8014 0.9902 -0.1435
850 1700 0.10625 0.3309 -1.6546 3.3091 -3.3091 1.6546 -0.3309 -2.8499 3.5382 -2.3086 0.783 -0.1095
950 1900 0.11875 0.2884 -1.4419 2.8837 -2.8837 1.4419 -0.2884 -2.5994 3.0408 -1.889 0.6155 -0.0832
1100 2200 0.1375 0.2334 -1.167 2.3339 -2.3339 1.167 -0.2334 -2.2249 2.3882 -1.3772 0.4238 -0.0544
1300 2600 0.1625 0.174 -0.8699 1.7399 -1.7399 0.8699 -0.174 -1.7275 1.6856 -0.8727 0.2515 -0.0302
1500 3000 0.1875 0.1275 -0.6377 1.2755 -1.2755 0.6377 -0.1275 -1.2323 1.1667 -0.5207 0.1459 -0.016
1700 3400 0.2125 0.0915 -0.4577 0.9153 -0.9153 0.4577 -0.0915 -0.7387 0.8245 -0.2723 0.0859 -0.0076
1900 3800 0.2375 0.0639 -0.3197 0.6394 -0.6394 0.3197 -0.0639 -0.2461 0.6546 -0.0842 0.059 -0.0022
2200 4400 0.275 0.0349 -0.1745 0.349 -0.349 0.1745 -0.0349 0.4923 0.7183 0.1733 0.0688 0.0047
2400 4800 0.3 0.0219 -0.1097 0.2194 -0.2194 0.1097 -0.0219 0.9853 0.9738 0.3864 0.1112 0.0113
2600 5200 0.325 0.0129 -0.0645 0.129 -0.129 0.0645 -0.0129 1.4797 1.4037 0.6809 0.1919 0.0221
2800 5600 0.35 0.0069 -0.0347 0.0693 -0.0693 0.0347 -0.0069 1.9759 2.0135 1.1026 0.3276 0.0407
3000 6000 0.375 0.0033 -0.0164 0.0328 -0.0328 0.0164 -0.0033 2.4744 2.811 1.7038 0.5444 0.0723
3300 6600 0.4125 0.0007 -0.0036 0.0072 -0.0072 0.0036 -0.0007 3.2269 4.3811 3.0782 1.1112 0.1641
3600 7200 0.45 0.0006 -0.003 0.006 -0.006 0.003 -0.0006 3.9845 6.4349 5.2536 2.1651 0.3599