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Only the sons are mentioned. Later in Genesis it says this:

(Genesis 5:4 NIV) After Seth was born, Adam lived 800 years and had other sons and daughters.

The first women to be mentioned by name after Eve are the wives of Lamech, the 7th generation from Adam:

(Genesis 4:17-19 NIV) Cain lay with his wife, and she became pregnant and gave birth to Enoch. Cain was then building a city, and he named it after his son Enoch. {18} To Enoch was born Irad, and Irad was the father of Mehujael, and Mehujael was the father of Methushael, and Methushael was the father of Lamech. {19} Lamech married two women, one named Adah and the other Zillah.

Yes you have hit it

Adam and Eve had at least five sons and two daughters. See Genesis chapters four and five. The only explanation of the growth of humanity has to be that Adam and Eve's children sometimes married each other, since there was no law from God about incest yet.

There was also no birth control. As more and more babies were born, it was no longer necessary to marry a brother or a sister. This is a simple answer. You will find more information if you start reading from Genesis 1 through Genesis 5.

Adam and Eve could have had 500 or more children during their long lifespans.