* 長男 (ちょうなん): This literally means "first son" and is the most common and direct way to say it.
You might also hear phrases like:
* 一番上の息子 (いちばんうえのむすこ): This means "the oldest son." While not exclusively referring to the *firstborn*, it often implies it.
The best choice depends on the nuance you want to convey. For most situations, 長男 (ちょうなん) is perfectly appropriate.