Dragonborn are humanoid
All playable races in 5e (with one exception)1 have the "Humanoid" type, as pointed out in the description of races in the basic rules:
Every character belongs to a race, one of the many intelligent humanoid species in the D&D world.
This is further supported by the description of the dragonborn race:
Dragonborn look very much like dragons standing erect in humanoid form, though they lack wings or a tail.
They may look like dragons, but they are not of the dragon type. They are humanoids.
Almost1 every playable race - humans, dragonborn, halflings, bugbears, kenku, tritons, etc. - is humanoid in nature.
1 The one exception to this general rule (as of this moment) is the centaur race from the Guildmaster's Guide to Ravnica (p. 15-16), which have the Fey trait:
Your creature type is fey, rather than humanoid.
As you can see, this supports the assumption that other playable races are humanoid, and clearly marks the centaur as an exception to this rule.