mathismath

from __future__ import division
from itertools import permutations

powers=[1, 2, 3, 4, 5]

for power_perm in list(permutations(powers)):

    elec = power_perm[0]
    dupl = power_perm[1]
    mstr = power_perm[2]
    gaze = power_perm[3]
    fire = power_perm[4]

    def two_of_dupl_spades(total):
        return total + 2**dupl

    def two_of_mstr_hearts(total):
        return total / 2**mstr

    def three_of_elec_hearts(total):
        return total / 3**elec

    def four_of_elec_clubs(total):
        return total * 4**elec

    def four_of_fire_diamonds(total):
        return total - 4**fire

    hand=[
        two_of_dupl_spades,
        two_of_mstr_hearts,
        three_of_elec_hearts,
        four_of_elec_clubs,
        four_of_fire_diamonds
    ]

    for play_order in list(permutations(hand)):

        r0 = ((2**fire - 4**dupl) * 5**fire / 5**dupl)

        r1 = play_order[0](((3**gaze + 3**fire) / 5**dupl))

        r2 = play_order[1](((3**mstr - 5**elec) * 2**fire))

        r3 = play_order[2](((5**fire - 4**mstr) + 5**mstr))

        r4 = play_order[3](((2**gaze / 4**dupl) * 4**gaze))
        
        r5 = play_order[4](((2**elec - 3**dupl) * 5**gaze))

        if (
            r0 == 100 and
            r1 == 6 and
            r2 == 28 and
            r3 == 496 and
            r4 == 8128 and
            r5 == 50000
        ):
            print("Power Values")
            print('elec: {}'.format(elec))
            print('dupl: {}'.format(dupl))
            print('mstr: {}'.format(mstr))
            print('gaze: {}'.format(gaze))
            print('fire: {}'.format(fire))
            print("")
            print("Play Order")
            for card in [f.__name__ for f in play_order]:
                print(card)

https://darocaro.github.io/puzzles/mathismath/mathismath

Result:

Power Values
elec: 2
dupl: 1
mstr: 4
gaze: 5
fire: 3

Play Order
three_of_elec_hearts
two_of_mstr_hearts
two_of_dupl_spades
four_of_fire_diamonds
four_of_elec_clubs