To solve the equation \( \ln(5x) + 3 = 7 \), first, we can isolate the natural logarithm:
\[ \ln(5x) = 7 - 3 \]
\[ \ln(5x) = 4 \]
Next, we can exponentiate both sides to eliminate the natural logarithm:
\[ 5x = e^4 \]
Now, to find \( x \), we divide both sides by 5:
\[ x = \frac{e^4}{5} \]
Calculating \( e^4 \) (using an approximate value of \( e \approx 2.71828\)):
\[ e^4 \approx 54.59815 \]
Substituting this value back in:
\[ x \approx \frac{54.59815}{5} \approx 10.91963 \]
Rounding this to two decimal places, we have:
\[ x \approx 10.92 \]
Therefore, the value of \( x \) is
\[ \boxed{10.92} \]