polyfit only get you the coefficients, you then have to actually evaluate some values to get the curve. An easy alternative is to use the function polyval (https://de.mathworks.com/help/matlab/ref/polyval.html), which will evaluate the given polynom for the given points. The following code should give you the result you would expect:
% store coordinates
x = [5.2 5.5 5.6 5.8];
y = [6.408 16.125 19.816 27.912];
% use polyfit to get coefficients of cubic
p = polyfit(x, y, 3);
yfit = polyval(p,x); % Evaluate polynomial coefficients p in values x
scatter(x, y, 'black');
hold on
plot(x,yfit, 'green');
