Here is the text of Quickdraw Synchron's effect:
>Once per turn: You can target 1 Level 5 or higher Synchro Monster in your GY; banish that target, and if you do, Special Summon this card from your hand.
Here are some of the reasons why you can Special Summon "Quickdraw Synchron" on your turn:
* The effect of "Quickdraw Synchron" does not specify that it can only be activated during your opponent's turn.
* The effect of "Quickdraw Synchron" does not have a cost, so you do not need to pay anything to activate it.
* The effect of "Quickdraw Synchron" does not target your opponent, so you do not need to worry about them being able to negate the effect.
Therefore, you can Special Summon "Quickdraw Synchron" from your hand to the field by banishing a Level 5 or higher Synchro Monster from your Graveyard, regardless of whose turn it is.