Being restrained causes the restrained character to attack with disadvantage for obvious reasons. However, would a spell caster (like a wizard) be able to still successfully cast a spell if it is purely vocal without rolling disadvantage? Do any of the books for 5e specify how or why this would be possible or not?
Also, one of my wizard players is debating that his character could still cast a spell that requires somatic and possibly other things like vocal. So, he's debating that with one hand (assuming that hand or part of the body isn't directly restrained) his character would still be able to cast a spell with no disadvantage as long as it his character's hand is free. I still believe that hand movement for a spell is possible but being restrained (unless specified on a single limb or body part) would be restraining and would cause any movement to be hindered and not as it naturally would be, meaning that casting a spell would not be as the wizard has practiced over and over and therefore cause disadvantage.
Best Answer
No, the player would attack with disadvantage.
As per the restrained condition:
This does not mention any exceptions for spell attacks, even ones with only verbal components. All attack rolls the creature makes while restrained then have disadvantage.
However, the point is nearly moot because there are no existing spells that are verbal only and require an attack roll. The Sorcerer metamagic subtle spell could be used to create such a case, however, which should be ruled as above.