ToE H5/HoF
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Level 1 Level 2 Level 3 Level 4 Level 5
Level 1
Direct Damage
Eldritch Arrow - Cost: 4

Shoots magic missile to deal non-physical damage to the selected enemy creature.

Eldritch Arrow
48+8*Power56+8*Power64+8*Power72+8*Power
Direct Damage
Stone spikes - Cost: 5

Deals earth damage to all creatures in target area (cross form)

Stone spikes
24+8*Power32+8*Power40+8*Power48+8*Power
Level 2
Direct Damage
Lightning Bolt - Cost: 5

Deals lightning damage to selected enemy unit.

Lightning Bolt
11+11*Power14+14*Power17+17*Power20+20*Power
Direct Damage
Ice Bolt - Cost: 6

Deals ice damage to selected enemy unit.

Ice Bolt
60+12*Power72+12*Power84+12*Power96+12*Power
Level 3
Direct Damage
Circle of Winter - Cost: 9

Deals ice damage to all units surrounding the target spot.

Circle of Winter
60+12*Power72+12*Power84+12*Power96+12*Power
Direct Damage
Fireball - Cost: 10

Deals fire damage to all units in the target area.

Fireball has a target area of 3x3.

Fireball
11+11*Power14+14*Power17+17*Power20+20*Power
Level 4
Direct Damage
Chain Lightning - Cost: 16

Deals massive lightning damage to several adjacent creatures (up to 4), starting with the selected one. Every next creature in the chain gets the half of the damage inflicted to the previous one. (The chain can hit the own creatures)

Chain Lightning
20+20*Power20+20*Power20+20*Power25+25*Power
Direct Damage
Meteor Shower - Cost: 19

Deals massive earth damage to all creatures in target area.

Meteor Shower has a target area of 5x5.

Meteor Shower
15+15*Power15+15*Power15+15*Power20+20*Power
Level 5
Direct Damage
Implosion - Cost: 18

Deals earth damage to a single targeted enemy unit.

Implosion
20+20*Power20+20*Power20+20*Power40+40*Power
Direct Damage
Armageddon - Cost: 20

Deals massive fire damage to all creatures and war machines on a battlefield and local physical damage in the place of fall.

Creatures in the center of the battlefield (4x4 square) are hit by the rock, and suffer extra physical damage (thus ignoring Magic Protection, Resistance and Immunities) equal to
5+5*Power 10+10*Power 15+15*Power 20+20*Power
Large creatures have to be completely inside the target area to be hit by the rock.
The Armaggedon itself damages all units not immune to Fire:

Armageddon
15+15*Power15+15*Power15+15*Power30+30*Power
This information comes from the Heroes V release version (v2.1).

Thanks to sfidanza for the work on this page.
Thanks to ThE_HyDrA for creating and looking after the Heroes 5 section of Age of Heroes!