Ah didnt realize you where doing a great weapon path. Gwm as a feat in general isnt very good, the bonus action swing is rare at best, and doesnt comba well with your smite spells. The -5+10 is unreliable at best and because of your smites any fight where this is useful you will not need the extra advantage. I'd say skip it and grab warcaster BB as a reaction and adv on your concentration saves is massive. Booming blade will actually out-damage extra attack usually and especially after level 5.
-math-
2d6+3+1d8=15.5
Lvl3 with gwf
2d6+3+2d8=20
Lvl5
-vs
2d6+3=11
4d6+6=22
A difference of 2 damage after extra attack if they stay adjacent, if they move add 4.5-9 damage.
Also you get to do some silly nova turns with a bit of setup. Turn before after you swing cast thunderous smite, then quicken a booming blade as a bonus actian and cast another one as normal. Youll have to move for the second one but youll do 6d6+4d8s+3 in one turn and if they move add 4d8. Because of the enemy control it gives you booming blade is far better than extra attack.
Please don't listen to Kithas's advice.
1. Reation attacks are extremely rare without PAM or Sentinel. So is forcing an enemy to move without eating an Opp Atk yourself, at least as a Vengeance Paladin.
2. His math is horribly wrong. Here is the real math:
Booming Blade
Levels 1-4: 2d6 (Average 8.33 with GWF) + 3 = 11.33 damage. If the target moves, add 1d8 (4.5) = 15.83 damage.
Levels 5-10: 2d6 (Average 8.33 with GWF) + 3 + 1d8 (4.5) = 15.33 damage. If the target moves, add 2d8 (9) = 24.33 damage
Regular
Levels 1-4: 2d6 (Average 8.33 with GWF) + 3 = 11.33 damage.
Levels 5-10: 4d6 (Average 16.66 with GWF) + 6 = 22.66 damage.
GWM
Levels 1-4: 2d6 (Average 8.33 with GWF) + 13 = 21.33 damage.
Levels 5-10: 4d6 (Average 16.66 with GWF) + 26 = 42.66 damage.
Simply put, there isn't even remotely a comparison. As a V-Pal, you get short rest rechargeable advantage. USE IT. So many V-Pals forget to use it. Oath of Enmity + GWM = dead BBEG. Additionally, BLESS!!!! Sweet baby jebus Bless yourself. Right from the get go Bless helps turn the tide in favor of GWM for enemies with AC 15 or less right from level 1. At level 4 when you boost STR (if you want damage) and then at level 5 with proficiency boost you're good at AC 16-17. If you Oath of Enmity an enemy, definitely use GWM.
Don't get me wrong, don't GWM on every strike, and definitely pick up BB/GFB (Greenflame Blade is significantly better because it doesn't rely on enemy movement and adds your Cha bonus). Kithas is absolutely correct that the SCAG cantrips help a ton. But without a way of generating Opp Atks, Warcaster would be a waste compared to GWM.