This is a bit of a data dump, but it's an interesting study in Phil Dawson's incredible 2016 season, in which he placed 41.5% of his kickoffs between the 0 and 5. His touchbacks are highlighted. I pulled these plays from NFL.com play-by-play using a Python script that searches for all instances of "kick" or "kicks":
(15:00 - 1st) P.Dawson kicks 63 yards from SF 35 to MIA 2. J.Grant to MIA 23 for 21 yards (A.Burbridge; M.Wilhoite). PENALTY on MIA-N.Hewitt
(9:46 - 1st) P.Dawson kicks 65 yards from SF 35 to MIA 0. K.Drake to MIA 21 for 21 yards (R.Streater; B.Bell).
(7:34 - 3rd) P.Dawson kicks 67 yards from SF 35 to MIA -2. K.Drake pushed ob at SF 24 for 78 yards (J.Tartt).
(7:42 - 4th) P.Dawson kicks 45 yards from SF 35 to MIA 20. K.Drake MUFFS catch
(2:15 - 4th) P.Dawson kicks 65 yards from SF 35 to MIA 0. J.Grant pushed ob at MIA 14 for 14 yards (B.Bell).
(1:32 - 2nd) P.Dawson kicks 64 yards from SF 35 to ARZ 1. B.Golden to ARZ 18 for 17 yards (J.Tartt).
(8:40 - 3rd) P.Dawson kicks 60 yards from SF 35 to ARZ 5. B.Golden to ARZ 23 for 18 yards (J.Tartt).
(1:55 - 4th) P.Dawson kicks 63 yards from SF 35 to ARZ 2. A.Ellington to ARZ 15 for 13 yards (M.Wilhoite).
(15:00 - 3rd) P.Dawson kicks 63 yards from SF 35 to LA 2. P.Cooper to LA 22 for 20 yards (C.Bradford). PENALTY on LA-B.Hager
(5:06 - 4th) P.Dawson kicks 69 yards from SF 35 to LA -4. P.Cooper to LA 30 for 34 yards (R.Streater).
(0:31 - 4th) P.Dawson kicks 62 yards from SF 20 to LA 18. P.Cooper to LA 42 for 24 yards (V.Sunseri; S.Draughn).
(14:52 - 1st) P.Dawson kicks 62 yards from SF 35 to DAL 3. L.Whitehead to DAL 31 for 28 yards (G.Hodges
(15:00 - 1st) P.Dawson kicks 61 yards from SF 35 to ARZ 4. J.Nelson to ARZ 43 for 39 yards (A.Burbridge).
(4:12 - 2nd) P.Dawson kicks 55 yards from SF 35 to ARZ 10. J.Nelson pushed ob at ARZ 24 for 14 yards (J.Hamm).
(1:54 - 3rd) P.Dawson kicks 65 yards from SF 35 to end zone
(0:03 - 1st) P.Dawson kicks 50 yards from 50 to TB 0. R.Smith to TB 6 for 6 yards (S.Draughn
(8:03 - 4th) P.Dawson kicks 59 yards from SF 35 to TB 6. A.Humphries to TB 23 for 17 yards (S.Skov).
(2:40 - 1st) P.Dawson kicks 55 yards from SF 35 to NE 10. Cy.Jones to NE 23 for 13 yards (M.Wilhoite).
(4:56 - 2nd) P.Dawson kicks 54 yards from SF 35 to NE 11. J.Develin to NE 25 for 14 yards (J.Shepherd; B.Bell). PENALTY on SF-R.Streater
(14:46 - 3rd) P.Dawson kicks 63 yards from SF 35 to NE 2. Cy.Jones to NE 22 for 20 yards (M.Wilhoite).
(14:50 - 1st) P.Dawson kicks 62 yards from SF 35 to NYJ 3. N.Marshall pushed ob at SF 44 for 53 yards (J.Ward). PENALTY on NYJ-A.Brown
(13:57 - 1st) P.Dawson kicks 25 yards from SF 35 to NYJ 40
(10:38 - 1st) P.Dawson kicks 58 yards from SF 35 to NYJ 7. N.Marshall to NYJ 24 for 17 yards (J.Tartt).
(5:39 - 2nd) P.Dawson kicks 64 yards from SF 35 to NYJ 1. N.Marshall to NYJ 25 for 24 yards (R.Streater).
(14:55 - 3rd) P.Dawson kicks 64 yards from SF 35 to SEA 1. J.McKissic to SEA 23 for 22 yards (J.Tartt).
(5:37 - 4th) P.Dawson kicks 46 yards from 50 to SEA 4. P.Richardson to SEA 14 for 10 yards (C.Bradford). PENALTY on SF-J.Tartt
(15:00 - 1st) P.Dawson kicks 65 yards from SF 35 to end zone
(9:41 - 2nd) P.Dawson kicks 57 yards from SF 35 to SEA 8. P.Richardson to SEA 27 for 19 yards (J.Tartt). SF-J.Ward was injured during the play. He is Out.
(7:50 - 4th) P.Dawson kicks 65 yards from SF 35 to end zone
(0:56 - 4th) P.Dawson kicks onside 26 yards from SF 35 to SEA 39. L.Willson MUFFS catch
(6:49 - 1st) P.Dawson kicks 60 yards from SF 35 to SD 5. C.Mager to SD 26 for 21 yards (M.Wilhoite).
(6:55 - 2nd) P.Dawson kicks 56 yards from SF 35 to CHI 9. D.Thompson to CHI 37 for 28 yards (J.Ward). FUMBLES (J.Ward)
(1:56 - 2nd) P.Dawson kicks 51 yards from SF 35 to CHI 14. P.Lasike to CHI 19 for 5 yards (A.Burbridge).
(15:00 - 3rd) P.Dawson kicks 65 yards from SF 35 to end zone
(15:00 - 1st) P.Dawson kicks 60 yards from SF 35 to CAR 5. T.Ginn pushed ob at CAR 28 for 23 yards (A.Burbridge). PENALTY on CAR-S.Thompson
(11:21 - 1st) P.Dawson kicks 62 yards from SF 35 to CAR 3. T.Ginn to CAR 20 for 17 yards (K.Reaser).
(10:02 - 2nd) P.Dawson kicks 60 yards from SF 35 to CAR 5. T.Ginn pushed ob at CAR 22 for 17 yards (J.Tartt).
(12:38 - 4th) P.Dawson kicks 62 yards from SF 35 to CAR 3. T.Ginn MUFFS catch
(12:31 - 4th) P.Dawson kicks 62 yards from SF 35 to CAR 3. T.Ginn to SF 38 for 59 yards (A.Burbridge).
(7:51 - 4th) P.Dawson kicks 60 yards from SF 35 to CAR 5. T.Ginn pushed ob at CAR 29 for 24 yards (K.Reaser).
Was inspired by this article from USA today