OR, you can forgo "Scapegoat" in the above combo and use your opponent's monsters instead, if you use "Super Polymerization".
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.
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.
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.