Turns out the NCAA decided to release the APRs after all, so here is the list of FBS teams in order of their 5-7 bowl eligibility - with a couple of notes:

First, Pac-12 teams that are 5-7 are currently not eligible to accept bowl bids by conference rule.
Second, Hawaii and Western Kentucky play 13 games; if they finish 6-7, they jump to the front of the list (the way Hawaii did last year), and if they finish 5-8, they are not bowl eligible.
Third, two pairs of teams (well, three, but one includes a Pac-12 team) have the same 4-year APR and the same 2020-21 1-year APR. The tiebreaker is their 2019-20 one-year APR, but the NCAA still has not made those public.

1. Mississippi, 999 (1000)
2. Clemson, 999 (994)
3. Alabama, 997
4. Northwestern, 995
5. Rice, 994 (1000)
6. Air Force, 994 (986)
7. * Washington, 993
8. Wisconsin, 992
9 (tie). Cincinnati, 991 (1000)
9 (tie). Ohio State, 991 (1000)
11. *Utah, 991 (988)
12. Boise State, 990 (990)
13. Wake Forest, 990 (988)
14. Louisville, 988 (986)
15. Minnesota, 988 (983)
16. Temple, 987
17. Iowa State, 986 (994)
18. Boston College, 986 (981)
19. Duke, 985 (981)
20. *Stanford, 985 (973)
21 (tie). Central Florida, 984 (990)
21 (tie). South Carolina, 984 (990)
23. UNLV, 984 (984)
24. Notre Dame, 984 (982)
25. Pittsburgh, 984 (975)
26. Virginia, 983 (1000)
27. Michigan State, 983 (993)
28. *Arizona State, 983 (984)
29. Auburn, 983 (983)
30. Missouri, 983 (974)
31. Miami, 982 (997)
32. Mississippi State, 982 (957)
33. Florida, 981
34. Army, 980 (985)
35. Michigan, 980 (982)
36. Georgia Tech, 979 (971)
37. Middle Tennessee State, 979 (957)
38. Eastern Michigan, 978 (991)
39. Kansas State, 978 (986)
40. Toledo, 978 (957)
41. North Carolina, 977 (1000)
42. Miami Ohio, 977 (987)
43. Rutgers, 977 (978)
44. SMU, 977 (970)
45. Liberty, 976 (993)
46. Indiana, 976 (987)
47. South Florida, 976 (968)
48. Arkansas State, 976 (967)
49. *USC, 975 (987)
50. *California, 975 (976)
51. Baylor, 975 (965)
52. North Carolina State, 974 (988)
53. Georgia State, 974 (987)
54. Wyoming, 974 (975)
55. West Virginia, 974 (971)
56. Oklahoma State, 973 (979)
57 (tie). Ball State, 973 (974)
57 (tie). *Oregon State, 973 (974)
59. Vanderbilt, 973 (969)
60. Nebraska, 972 (976)
61. Memphis, 972 (934)
62. Kentucky, 971 (981)
63. Texas, 971 (969)
64. San Diego State, 971 (960)
65. Tulane, 970 (987)
66. Purdue, 970 (978)
67. Nevada, 970 (975)
68. Connecticut, 970 (958)
69. Navy, 970 (948)
70. Penn State, 970 (937)
71. Illinois, 969 (975)
72. Utah State, 969 (962)
73. Appalachian State, 968 (985)
74. Buffalo, 968 (976)
75. Oklahoma, 968 (971)
76. Iowa, 968 (958)
77. Georgia, 967
78. Florida International, 966
79. Ohio, 965 (958)
80. *Arizona, 965 (951)
81. Coastal Carolina, 964 (994)
82. Virginia Tech, 964 (981)
83. Fresno State, 964 (951)
84. Bowling Green, 963 (978)
85. Marshall, 963 (964)
86. East Carolina, 961 (1000)
87. San Jose State, 961 (979)
88. Kansas, 961 (943)
89. *Western Kentucky, 960 (968)
90. Kent State, 960 (942)
91. *Oregon, 960 (939)
92. North Texas, 960 (936)
93. *Washington State, 959
94. Florida State, 958 (987)
95. Texas A&M, 958 (956)
96. Louisiana Tech, 958 (951)
97. Central Michigan, 958 (940)
98. Arkansas, 957 (981)
99. Northern Illinois, 957 (937)
100. Syracuse, 957 (929)
101. Texas State, 956 (991)
102. Charlotte, 956 (975)
103. TCU, 955 (973)
104. Old Dominion, 955 (958)
105. Texas Tech, 955 (944)
106. Louisiana, 955 (943)
107. *Colorado, 954 (978)
108. Colorado State, 954 (961)
109. Akron, 954 (937)
110. Texas-San Antonio, 953 (963)
111. BYU, 953 (959)
112. Troy, 952 (975)
113. Georgia Southern, 952 (945)
114. Massachusetts, 951
115. Florida Atlantic, 949 (961)
116. South Alabama, 949 (953)
117. Houston, 948 (934)
118. Louisiana-Monroe, 948 (911)
119. *UCLA, 947
120. *Hawaii, 946 (947)
121. Tennessee, 946 (944)
122. Alabama-Birmingham, 945
123. Maryland, 944
124. New Mexico State, 940
125. Tulsa, 939
126. Western Michigan, 938
127. New Mexico, 935
128. UTEP, 934 (935)
129. Southern Mississippi, 934 (899)
130. LSU, 933