With Thirsting Blade at 5th level, your options are:
- Eldritch Blast twice with Eldritch Ray, Eldritch Scythe, or Eldritch Whip; or 2d10 damage with one Eldritch Disturbance.
- Attack twice with your melee weapon.
- Eldritch Blast once, and attack once with your melee weapon.
For option 1, with Eldritch Scythe and Agonizing Blast, with Warlock spellcasting ability modifier is +4, and if you cast Hex as a bonus action, the damage you do assuming that you hit, but not critically, is (d8 + 4 WIS + 1 + d6 Hex) x2 = 26.0 average to the primary target and (d8 + 4 WIS + 1) x2 / 2 = 9.5 on average to a second target within reach.
For option 2, let's assume your Warlock spellcasting ability modifier is +4, and that you cast Hex as a bonus action. If your melee weapon is say a greatsword+1, and you have Lifedrinker, using it for both attacks, you do 2x(2d6 + 1 magic item bonus + 4 modifier + 4 Lifedrinker + d6 Hex) = 39 average damage, assuming that you hit but not critically.
For option 3, it is midway between 1 and 2.
To maximize melee damage against a single target, hitting them with your pact weapon, thirsting blade, and and lifedrinker is the way to go (option 2). If you want to push them around on the battlefield with say Repelling Blast, then option 3 is best - hit them once with the melee weapon, then push them 10' back. Option 1 doesn't do more damage until level 11+.
If you really want to maximize your melee damage output, you dual wield, and on the second round you can apply the Hex d6 bonus damage to all four attacks - two with your main hand, and two with your off-hand, per the A5E two-weapon fighting rule, "
If you have the Extra Attack feature, you can use your bonus action to make two attacks with the weapon in your off-hand."
Note that Hex is listed as a Warlock spell in
Spells | Level Up, even though it is not in the Adventurer's Guide. If your DM permits Spirit Shroud from Tasha's Cauldron of Everything, that scales up even better for damage output than Hex. Spirit Shroud does +2d8 damage to a target within 10', when you cast it as a 5th level spell, at Warlock level 9+.
Until character level 17, Eldritch Blast doesn't do more average damage per round than when you are using Polearm Savant with a polearm for 3 attacks, or two-weapon fighting for 4 attacks. However, you are missing out on all the fun stuff that you can do with Eldritch Blast such as 10' push/pull, grapple, or paralyze, if you take the right Eldritch Invocations.
In my opinion, Eldritch Scythe may be better used with say an Imp familiar and Pact of the Chain at lower levels, which states, "
When you use Eldritch Scythe, you can choose to deliver the attack through your familiar as though you had cast a spell with a range of Touch." (Your familiar can get killed off pretty quickly at higher levels, if you send it out to attack in that fashion.) Other than that, I think that Eldritch Ray is a better choice for your Eldritch Blast; but Eldritch Scythe may well be worth taking with Versatile Blast at some point.