Answer: four more tests


Using fractions
Initial score: $\dfrac15$

After 1 test: $\dfrac{1+5}{5+5}=\dfrac{6}{10}=60\%$

After 2 tests: $\dfrac{6+5}{10+5}=\dfrac{11}{15}\lt\dfrac{12}{15}$ which is equal to $80\%$

After 3 tests: $\dfrac{11+5}{15+5}=\dfrac{16}{20}=80\%$

After 4 tests: more than $80\%$

So she needs to take four more tests to obtain an average mark of more than $80$%.


Using averages
$\frac15=20\%$, get $100\%$ to reach target of $80\%$

$20\%$ is $60\%$ below $80\%$
                            $80\%$ is $20\%$ below $100\%$
                                       $20\%\times3=60\%$
                                       $20\%$ above three times to balance $60\%$ below

So after 3 more tests the average will be $80\%$
After the fourth test it will be above $80\%$