My own viewing order, compiled from a multitude of sources and my own opinions on continuity issues as I watch the series.
Sources:
- http://www.midwinter.com/lurk/countries/master/eplist.html
- http://scifi.stackexchange.com/a/10015/31492
- http://scifi.stackexchange.com/a/21381/31492
- http://www.b5tv.com/showthread.php?t=11675
- http://johan.kiviniemi.name/blag/b5/
- The Gathering
1x01
Midnight on the Firing Line1x02
Soul Hunter1x03
Born to the Purple1x04
Infection1x05
The Parliament of Dreams1x06
Mind War1x07
The War Prayer1x08
And The Sky Full Of Stars1x09
Deathwalker1x10
Believers1x11
Survivors1x12
By Any Means Necessary1x13
Signs and Portents1x14
TKO1x15
Grail1x16
Eyes1x18
A Voice in the Wilderness part 11x19
A Voice in the Wilderness part 21x20
Babylon Squared1x21
The Quality of Mercy1x17
Legacies1x22
Chrysalis
2x01
Points of Departure2x02
Revelations2x03
The Geometry of Shadows2x04
A Distant Star2x05
The Long Dark2x06
A Spider in the Web2x08
A Race Through Dark Places2x07
Soul Mates2x09
The Coming of Shadows2x10
GROPOS2x11
All Alone in the Night2x12
Acts of Sacrifice2x13
Hunter, Prey2x14
There All the Honor Lies2x15
And Now For a Word2x17
Knives2x16
In the Shadow of Z'ha'dum2x18
Confessions and Lamentations2x19
Divided Loyalties2x20
The Long, Twilight Struggle2x21
Comes the Inquisitor2x22
The Fall of Night
3x01
Matters of Honor3x02
Convictions3x03
A Day in the Strife3x04
Passing Through Gethsemane3x05
Voices of Authority3x06
Dust to Dust3x07
Exogenesis3x08
Messages from Earth3x09
Point of No Return3x10
Severed Dreams3x11
Ceremonies of Light and Dark3x13
A Late Delivery From Avalon3x12
Sic Transit Vir3x14
Ship of Tears3x15
Interludes and Examinations3x18
Walkabout3x16
War Without End, Part One3x17
War Without End, Part Two3x19
Grey 17 Is Missing3x20
And the Rock Cried Out, No Hiding Place3x21
Shadow Dancing3x22
Z'ha'dum
4x01
The Hour of the Wolf4x02
Whatever Happened to Mr. Garibaldi?4x03
The Summoning4x04
Falling Toward Apotheosis4x05
The Long Night4x06
Into the Fire4x07
Epiphanies- (First 2 minutes only, stop after scene with Zach)
4x09
Atonement - Thirdspace
4x08
The Illusion of Truth4x09
Atonement- In The Beginning
4x10
Racing Mars4x11
Lines of Communication4x12
Conflicts of Interest4x13
Rumors, Bargains and Lies4x14
Moments of Transition4x15
No Surrender, No Retreat4x16
The Exercise of Vital Powers4x17
The Face of the Enemy4x18
Intersections in Real Time4x19
Between the Darkness and the Light4x20
Endgame4x21
Rising Star4x22
The Deconstruction of Falling Stars
You can pretty much consider this entire season as one long epilogue. It's enjoyable, but the main storyline wraps up after season 4, so don't set your expectations too high for this season.
5x01
No Compromises5x02
The Very Long Night of Londo Mollari5x03
The Paragon of Animals5x04
A View from the Gallery5x05
Learning Curve5x06
Strange Relations5x07
Secrets of the Soul5x09
In the Kingdom of the Blind5x10
A Tragedy of Telepaths5x11
Phoenix Rising5x12
The Ragged Edge5x08
Day of the Dead5x13
The Corps is Mother, The Corps is Father5x14
Meditations on the Abyss5x15
Darkness Ascending5x16
And All My Dreams, Torn Asunder5x17
Movements of Fire and Shadow5x18
The Fall of Centauri Prime5x19
Wheel of Fire5x20
Objects in Motion5x21
Objects at Rest- [1 year later] River of Souls
- [2 years later] (not really worth it IMO, and has chronology issues) The Legend of the Rangers
- [5 years later] A Call To Arms
- [10 years later] (skip the first episode, it's ridiculous) The Lost Tales / Voices in the Dark
- [20 years later]
5x22
Sleeping in Light
I didn't watch any of these, but if you want to, they go after A Call To Arms at the end of Season 5
Crusade e01-e13 (see: Lurker's Guide for order)
FYI, the most popular Babylon 5 Viewing Orders for all TV Episodes and Movies are now listed here: https://babylon5.fandom.com/wiki/Viewing_Order