The most straightforward way would be to compute each difference and use a regression model using the differences as predictors of YA minus YB. This could be done with multiple regression, but it might be more sensible to bootstrap the regression model.

A slightly more formal approach would be to use contrasts to capture the differences and to form a contrast to test the differences in contrasts. The advantage of this approach is that you can constrain the original contrast weights to have equal variance so that one doesn't explain more of your outcome simply because it is more variable. This may or may not be desirable.

I'm not sure of a more bespoke model than these but there might be one.

Thank you Sir for a straightforward and easy to understand answer.

I agree with Thom, regression model is the best solution.

I think with 5 observations for each country that you're not going to get much useful trying to build a multiple regression model.

I don't have an elegant solution, but here's what I'm thinking.

The first step might be to see if there is a trend for each of the y variables.  You might try Mann-Kendall for this. With 5 observations even this test might not be very conclusive.  Minimally, you might have to relax your alpha value (to decide what is a significant p-value) to 0.15 or 0.20.*

For your independent variables, I think you'll have to decide if it makes sense that the effect of the variable varies from year to year.  To wit:

Let's call an A type variable one whose effect will vary meaningfully year to year.  For example, perhaps money spent on education devoted to disease avoidance is expected to have an effect on the rate of infection in the same year. 

Let's call type B a variable that may have an overall effect on the dependent variable but whose year-to-year variation won't make a difference.  For example the overall GDP or education level of a county may affect the infection rate, but a [small] change in GDP one year to the next won't make a difference in the infection rate, because its effect may take decades to matter.

For type A variables, you might try Kendall or Spearman correlation between the independent variable and the dependent variable.  Again, you may need to relax your alpha to 0.15 or 0.20 for the number of observations you have.  If the correlation exists for both countries, it may be meaningful in the explaining the difference between the countries.  But you will also want to look at the trend of the independent variable itself as well.

For type B variables, I think you want to see if there is a difference in independent variables between the countries, with a test analogous to a Mann-Whitney test.  If there is a meaningful difference, the variable might be meaningful in explaining the difference in Y between the countries.

Of course, none of these correlations or tests will prove a cause-and-effect.

And, of course, with 5 observations, any conclusions are pretty speculative.

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*  So if the data you present are real, if you want to use an alpha of 0.25, there is probably a positive trend for YA (MannKendall, tau = 0.6, p = 0.22), and there is probably a negative trend for YB (MannKendall, tau = - 0.8, p = 0.09).