To add the numbers \( 3.596 \times 10^{5} \) and \( 5.03 \times 10^{6} \), first align the exponents. Convert \( 3.596 \times 10^{5} \) to \( 0.3596 \times 10^{6} \).
Add the coefficients of the aligned numbers: \[ 0.3596 + 5.03 = 5.3896 \]
Combine the sum of the coefficients with the exponent: \[ 5.3896 \times 10^{6} \]
\(\boxed{5.3896 \times 10^{6}}\)
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