To add \(5.3 \times 10^5\) and \(3.8 \times 10^4\), we first need to express both numbers in terms of the same power of ten.
We can convert \(3.8 \times 10^4\) to the same power of ten as \(5.3 \times 10^5\):
\[ 3.8 \times 10^4 = 0.38 \times 10^5 \]
Now, we can add:
\[ 5.3 \times 10^5 + 0.38 \times 10^5 = (5.3 + 0.38) \times 10^5 = 5.68 \times 10^5 \]
Thus, the sum of \(5.3 \times 10^5\) and \(3.8 \times 10^4\) in scientific notation is:
\[ \boxed{5.68 \times 10^5} \]
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