OR, you can forgo "Scapegoat" in the above combo and use your opponent's monsters instead, if you use "Super Polymerization"(Traditional Format).
OR, you could use "D. Tribe" and/or "DNA Surgery" (declaring Dragon-Type) with "Scapegoat" and "Fusion Gate" "Field Spell Card" on the field, in order to Summon "Five-Headed Dragon" so effectively and effortlessly indeed.
In a "Gandora" Deck, use "Future Fusion" to reveal this card and send 5 Dragons, including 3 differently-named "Gandora" monsters to the Graveyard. Even if you don't summon this card, "Gandora Giga Rays the Dragon of Destruction" will be able to apply its third effect.
If you have "Lord of D." or "King Dragun" on the field, "Five-Headed Dragon" can't be targeted by Spell, Trap or monster effects.
"Painful Choice" can easily deposit Dragons into the Graveyard for the usage of "Dragon's Mirror".
This is a great card to use as a Tribute for "The Tyrant Neptune", as it can gain this card's ATK and effect. Tributing "Hardened Armed Dragon" in addition to this combo will grant "The Tyrant Neptune" additional protection.
You can use "DNA Surgery" along with "Super Polymerization" to Summon "Five-Headed Dragon". Use "DNA Surgery" to declare all monsters on the field to Dragon-Type, then use "Super Polymerization" to either on your opponent's or your own monsters to bring out "Five-Headed Dragon". It is also very effective to use your opponent's monsters as Fusion Materials, so that way, they won't have any monsters to defend from a direct attack.
In a Dragon Ruler/Lightsworn Deck, you can Special Summon all 4 of the Dragon Rulers after using "Judgment Dragon's" effect to destroy all other cards on the field. After attacking with them(Or not, if their LP is already 5000 or less), you can Fusion Summon this card with "Flash Fusion" and attack directly for an OTK.
You can also banish all 5 of them with "Dragon's Mirror" to summon this card.