5. Although she runs fast, she doesn't win. (despite)

=>Despite running fast,she doesn't win.

7. Even though Linda stayed up late, she got up early. (Despite)

=>Despite staying up late,she got up early.

11. She got up early, but she missed the bus. (although)

=>Although she got up early,she missed the bus.

12. In spite of eating much, Tom doesn't feel tired. (even though)

=>Even though Tom eats much, he doesn't feel tired.

CT:
Despite=In spite of = Even though=Though=Although: Mặc dù.....

In spite of/Despite +N/Ving/the fact that....,+S+V+O

Although/....+S+V+O,+S+V+O

$5$. Despite running fast,she doesn't win.

$6$. Despite staying up late, Linda got up early.

$7$. Although she got up early,she missed the bus.

$8$. Even though Tom eats much, he doesn't feel tired.

`->`In spite of/Despite + N/V-ing/N phrase/......,+S + V + O

`->`Although/Even though/..... + S + V + O, S + V + O