Step 1 :Let's denote the number of students who studied in the most popular host country as \(x\) and the number of students who studied in the second most popular host country as \(y\).
Step 2 :We know that the total number of students who studied in both countries is 57,918. So, we can write this as an equation: \(x + y = 57,918\).
Step 3 :We also know that there were 5890 more students who studied in the most popular host country than in the second most popular host country. We can write this as another equation: \(x = y + 5890\).
Step 4 :We can solve this system of equations to find the values of \(x\) and \(y\).
Step 5 :By solving the equations, we find that \(x = 31904\) and \(y = 26014\).
Step 6 :Final Answer: There were \(\boxed{31904}\) students who studied abroad in the most popular host country and \(\boxed{26014}\) students who studied abroad in the second most popular host country.