Let's say that my opponent won't cast any spells during the first 5 turns of a duel. What is the best combination of spells to do as much damage as possible in that time?
First of all, let's review all the damage spells that can be cast in 5 turns or less, one by one, considering their casting time and the damage that they cause by the fifth turn:
Summon Ice/Fire Elemental: 5 turns to cast and 3 damage for one turn
Lightning bolt (normal version) or Fireball: 5 turns to cast and 5 damage (one off)
Summon Troll: 5 turns to cast and 3 damage for one turn
Summon Ogre: 4 turns to cast and 2 damage for 2 turns (total: 4 damage)
Magic Missile: 2 turns to cast and one damage (one off)
Summon Goblin: 3 turns to cast and 1 damage for 3 turns (total: 3 damage)
Fire/Ice Storm or Lightning Bolt (short version): 4 turns to cast (but last movement involves both hands) and 5 damage (one off)
Cause Light Wounds: 3 turns to cast and 2 damage (one off)
Cause Heavy Wounds: 4 turns to cast and 3 damage (one off)
Stab (>): One damage per turn (total: 5) - you can stab with only one hand each turn
It appears that, in general, the best "efficiency" you can achieve is one damage per turn (per hand), with the exception of Fire/Ice Storm (that however require 2 hands for last movement and affect everybody, including the caster) and the short version of Lightning Bolt (that however requires 2 hands for the last movement and can be used only once per match).
So, at best you'll be able to cause 10 damage to your opponent in 5 turns, through a relatively small number of combinations; you need to use the "highest efficiency" ones: Lightning Bolt (normal version), Fireball and Stab. You can mix and match them as you like.
You can't get the best efficiency (in five turns) from the short version of the Lightning Bolt because, even if you continuously stab with your free hand, in the last turn you should stab with both hands to cause the 10th point of damage, but you can only stab with one hand, so you'd stop at 9 damage.
Other "high efficiency combinations" are Summon Ogre + one Stab (total: 5 damage, like the previous ones), or Summon Goblin + two Stabs (again, 5 damage). The maximum damage in 5 turns is still 10; other combinations cause less damage in 5 turns.