After her second test her average mark is $\frac{6}{10}$, after her third test her average is $\frac{11}{15}$, after her fourth it is $\frac{16}{20}=\frac{4}{5}=80$% exactly and after the fifth it is $\frac{21}{25}=84$%.

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

*This problem is taken from the UKMT Mathematical Challenges.*