Table 3.3. Filter coefficients for a 5th order low-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
50 100 0.0125 2.74E-9 1.37E-8 2.74E-8 2.74E-8 1.37E-8 2.74E-9 -4.8729 9.4997 -9.2613 4.5152 -0.8807
60 120 0.015 6.74E-9 3.37E-8 6.74E-8 6.74E-8 3.37E-8 6.74E-9 -4.8475 9.4016 -9.1192 4.4237 -0.8585
70 140 0.0175 1.44E-8 7.19E-8 1.44E-7 1.44E-7 7.19E-8 1.44E-8 -4.8221 9.3041 -8.9789 4.3339 -0.837
80 160 0.02 2.77E-8 1.38E-7 2.77E-7 2.77E-7 1.38E-7 2.77E-8 -4.7967 9.2072 -8.8404 4.2458 -0.816
90 180 0.0225 4.93E-8 2.46E-7 4.93E-7 4.93E-7 2.46E-7 4.93E-8 -4.7713 9.111 -8.7036 4.1594 -0.7955
100 200 0.025 8.25E-8 4.12E-7 8.25E-7 8.25E-7 4.12E-7 8.25E-8 -4.7459 9.0154 -8.5687 4.0746 -0.7755
120 240 0.03 2.00E-7 1.00E-6 2.00E-6 2.00E-6 1.00E-6 2.00E-7 -4.695 8.8261 -8.304 3.9099 -0.737
140 280 0.035 4.22E-7 2.11E-6 4.23E-6 4.23E-6 2.11E-6 4.22E-7 -4.6442 8.6394 -8.0461 3.7514 -0.7004
160 320 0.04 8.04E-7 4.02E-6 8.04E-6 8.04E-6 4.02E-6 8.04E-7 -4.5934 8.4551 -7.7949 3.5989 -0.6657
180 360 0.045 1.42E-6 7.08E-6 1.42E-5 1.42E-5 7.08E-6 1.42E-6 -4.5426 8.2733 -7.5503 3.4522 -0.6326
200 400 0.05 2.34E-6 1.17E-5 2.34E-5 2.34E-5 1.17E-5 2.34E-6 -4.4918 8.0941 -7.3121 3.311 -0.6011
250 500 0.0625 6.74E-6 3.37E-5 6.74E-5 6.74E-5 3.37E-5 6.74E-6 -4.3649 7.6566 -6.7437 2.9813 -0.5291
300 600 0.075 1.58E-5 7.92E-5 1.59E-4 1.59E-4 7.92E-5 1.58E-5 -4.238 7.2344 -6.2125 2.6821 -0.4655
350 700 0.0875 3.24E-5 1.62E-4 3.24E-4 3.24E-4 1.62E-4 3.24E-5 -4.1112 6.8272 -5.7164 2.4109 -0.4094
400 800 0.1 5.98E-5 2.99E-4 5.98E-4 5.98E-4 2.99E-4 5.98E-5 -3.9845 6.4349 -5.2536 2.1651 -0.3599
450 900 0.1125 0.0001 0.0005 0.001 0.001 0.0005 0.0001 -3.858 6.0572 -4.8222 1.9426 -0.3163
500 1000 0.125 0.0002 0.0008 0.0016 0.0016 0.0008 0.0002 -3.7315 5.6939 -4.4205 1.7411 -0.2778
600 1200 0.15 0.0004 0.0018 0.0037 0.0037 0.0018 0.0004 -3.4789 5.0098 -3.6995 1.3942 -0.2138
700 1400 0.175 0.0007 0.0036 0.0072 0.0072 0.0036 0.0007 -3.2269 4.3811 -3.0782 1.1112 -0.1641
800 1600 0.2 0.0013 0.0064 0.0128 0.0128 0.0064 0.0013 -2.9754 3.806 -2.5453 0.8811 -0.1254
900 1800 0.225 0.0021 0.0106 0.0211 0.0211 0.0106 0.0021 -2.7246 3.2832 -2.0902 0.6948 -0.0955
1000 2000 0.25 0.0033 0.0164 0.0328 0.0328 0.0164 0.0033 -2.4744 2.811 -1.7038 0.5444 -0.0723
1200 2400 0.3 0.0069 0.0347 0.0693 0.0693 0.0347 0.0069 -1.9759 2.0135 -1.1026 0.3276 -0.0407
1400 2800 0.35 0.0129 0.0645 0.129 0.129 0.0645 0.0129 -1.4797 1.4037 -0.6809 0.1919 -0.0221
1600 3200 0.4 0.0219 0.1097 0.2194 0.2194 0.1097 0.0219 -0.9853 0.9738 -0.3864 0.1112 -0.0113
1800 3600 0.45 0.0349 0.1745 0.349 0.349 0.1745 0.0349 -0.4923 0.7183 -0.1733 0.0688 -0.0047
2000 4000 0.5 0.0528 0.2639 0.5279 0.5279 0.2639 0.0528 0 0.6334 0 0.0557 0
2250 4500 0.5625 0.0839 0.4196 0.8392 0.8392 0.4196 0.0839 0.6155 0.766 0.2213 0.0764 0.0061
2500 5000 0.625 0.1275 0.6377 1.2755 1.2755 0.6377 0.1275 1.2323 1.1667 0.5207 0.1459 0.016
2750 5500 0.6875 0.1875 0.9375 1.8751 1.8751 0.9375 0.1875 1.8516 1.8438 0.9825 0.2873 0.0351
3000 6000 0.75 0.2689 1.3447 2.6894 2.6894 1.3447 0.2689 2.4744 2.811 1.7038 0.5444 0.0723
3250 6500 0.8125 0.3788 1.8942 3.7885 3.7885 1.8942 0.3788 3.1011 4.0869 2.8014 0.9902 0.1435
3500 7000 0.875 0.527 2.6351 5.2702 5.2702 2.6351 0.527 3.7315 5.6939 4.4205 1.7411 0.2778
3750 7500 0.9375 0.7274 3.6368 7.2736 7.2736 3.6368 0.7274 4.3649 7.6566 6.7437 2.9813 0.5291