We have 5374 microbes in a dish.
Then, 3224 more microbes are present in the dish.
We have to add them without a calculator by rounding the numbers to the nearest hundred:
[tex]\begin{gathered} n=5374+3224 \\ n\approx5400+3200 \\ n\approx8600 \end{gathered}[/tex]Answer: the new number of microbes in the dish is approximately 8600.