All listed names are in EDF5.
EDF4.1 includes everything that's not in 5.
Exceptions are noted.

--EDF5 Music--
BGM_E5S01_Title
BGM_E5S02_EDFHonbu
BGM_E5S03_Edit --Same as BGM_E4S03_EditGamen
BGM_E5S04_OnlineLobby
BGM_E5S05_Staffroll
BGM_E5S05_Staffroll_cn
BGM_E5S05_Staffroll_en
BGM_E5S05_Staffroll_kr
BGM_E5S06_OpTelop --Same as BGM_E4S07_OpTelop
BGM_E5S07_EndingTelop
BGM_E5S08_EndingTelopOnline
BGM_Sinkou_Edtelop --Same as BGM_E4S08_EndingTelop; Mistakenly uses EDF2017's naming scheme
BGM_E5D01_UchujinKouka
BGM_E5D02_Daikaiju --Same as BGM_Demo_BigMonster
BGM_E5M01_MainBGM_BeforeHalf
BGM_E5M02_MainBGM_AfterHalf
BGM_E5M03_ChiteiTanken
BGM_E5M04_RansenGekisen
BGM_E5M05_HisounaruShingun
BGM_E5M06_KirikakaruMachi --Foggy/Night battle?
BGM_E5M07_Totsugekiseyo  --That one song that plays at the end of mission 3 where the nix activate
BGM_E5M08_KyuuhennSuruSenjou
BGM_E5M09_Heion
BGM_E5M10_Daikaiju
BGM_E5M11_MotherShip
BGM_E5M12_ShouriNoKizashi  --EDF! EDF! EDF!
BGM_E5M13_KyuuhennSuruSenjou_Kouhan --That tense theme used in certain parts
BGM_E5M14_Tutorial
BGM_E5M15_FinalMission
BGM_E4M16_TutorialHeiwa --Note that it's mistakenly E4
--EDF4.1 Music--
BGM_E4S01_TitleGamen
BGM_E4S02_EDFHonbu
BGM_E4S03_EditGamen
BGM_E4S04_OnlineLobby
BGM_E4S05_TaisenMenu
BGM_E4S06_StaffRoll --Japanese version in 4.1; Same as BGM_E4EX0_LetsGoEDF in 5
BGM_E4S07_OpTelop
BGM_E4S08_EndingTelop
BGM_E4D01_KyodaiAriShuurai
BGM_E4D02_UFOShuurai
BGM_E4D03_HikouYousai
BGM_E4D04_KyodaiRobotYousai
BGM_E4D05_ShinMotherShipToujou
BGM_E4EX0_LetsGoEDF
BGM_E4M01_MainBGM_A
BGM_E4M01_MainBGM_B
BGM_E4M02_RyuNoMure
BGM_E4M03_Hoshoku
BGM_E4M04_Taigunarawaru
BGM_E4M05_Totsugeki
BGM_E4M05_Totsugeki_old
BGM_E4M05_Totsugeki_v2
BGM_E4M05_Totsugeki_v3
BGM_E4M06_HisounaTatakai
BGM_E4M07_ChiteiShinko
BGM_E4M08_EarthEater
--EDF2017 Music, a few are 4.1's remixes--
BGM_Sinkou_intermission
BGM_Sinkou_OPtelop
BGM_Sinkou_taisenmenu
BGM_Sinkou_title
BGM_Demo_2legTank
BGM_Demo_4legTank
BGM_Demo_BigMonster
BGM_Demo_Kyodaiari
BGM_Demo_MotherShip
BGM_Demo_UFOencount
BGM_inGame_chiteishinbu
BGM_inGame_Gekitou
BGM_inGame_HisounaTatakai
BGM_inGame_KougekiKaishi
BGM_inGame_Kyodaiari
BGM_inGame_Mothership
BGM_inGame_Soutousen
BGM_inGame_Spider
BGM_inGame_UFOstage
--EDF2 Music, looped versions from Portable--
BGM_tikyuu2_enbansyuurai
BGM_tikyuu2_mothership
BGM_tikyuu2_saisyuukessen_wakusei
--Mission End Fanfares--
Jingle_MissionCleared
Jingle_MissionCleared_EDF4 --Not in 4.1
Jingle_MissionClearedFinal
Jingle_MissionEscape --Not in 4.1
Jingle_MissionFailed
Jingle_OnlineClearedFinal
Jingle_TGScomingSoon