You need to calculate where each month falls, in terms of hours:
ttk = datetime(2019,1:13,1);
set(gca, 'xtick', hours(ttk-datetime(2019,1,1)), 'xticklabel', cellstr(datestr(ttk,'mmm')))
Check the specific year of your data; the alignment will be different in leap years vs non-leap years.
Alternatively, if you actually specify datetime values for your x-values, Matlab will create a date axis that automatically labels things appropriately:
t = datetime(2019,1,1) + hours(1:8760);
plot(t, A(1:8760,5)');
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