5. (5 points) There are three simplest true fractions, the ratio of their numerators is $3: 2: 4$, and the ratio of their denominators is $5: 9: 15$. After adding these three fractions and simplifying, the result is $\frac{28}{45}$. What is the sum of the denominators of the three fractions? $\qquad$ .
【Analysis】According to the problem, we can assume that these three simplest proper fractions are $\frac{3 \mathrm{a}}{5 \mathrm{~b}} 、 \frac{2 \mathrm{a}}{9 \mathrm{~b}} 、 \frac{4 \mathrm{a}}{15 \mathrm{~b}}$, where $a 、 b$ are coprime, and then find the values of $a 、 b$; finally, substitute them into the denominators of the three simplest proper fractions to find each denominator.

【Solution】Solution: According to the problem, assume that these three simplest proper fractions are $\frac{3 \mathrm{a}}{5 \mathrm{~b}} 、 \frac{2 \mathrm{a}}{9 \mathrm{~b}} 、 \frac{4 \mathrm{a}}{15 \mathrm{~b}}$, where $a 、 b$ are coprime.
$$
\begin{array}{l}
\because \frac{3 \mathrm{a}}{5 \mathrm{~b}}+\frac{2 \mathrm{a}}{9 \mathrm{~b}}+\frac{4 \mathrm{a}}{15 \mathrm{~b}}=\frac{49 \mathrm{a}}{45 \mathrm{~b}}=\frac{28}{45}, \\
\therefore a=4, b=7 .
\end{array}
$$
$\therefore$ The sum of the denominators of the three fractions is $7 \times(5+9+15)=203$.
Therefore, the answer is: 203.