The cost of a mango is 8 each, while a guava costs 6 each. A woman spends a total of 52 on these fruits. How many mangoes and guavas did she buy?

Let the number of mangoes purchased be $m$ and the number of guavas purchased be $g$.
Given the cost constraints:

$$8m+6g=52$$

We can verify the options to check which set satisfies the equation:

* Option A: 5 mangoes and 2 guavas

$$8(5)+6(2)=40+12=52$$

This matches the total expenditure.
* Option B: 5 mangoes and 1 guava

$$8(5)+6(1)=40+6=46\ne 52$$

* Option C: 3 mangoes and 4 guavas

$$8(3)+6(4)=24+24=48\ne 52$$

* Option D: 4 mangoes and 3 guavas

$$8(4)+6(3)=32+18=50\ne 52$$

Hence, Option A is the correct answer.