If a : b = c : d = e : f = 5 : 7, then what is the ratio (3a + 5c + 11e) : (3b + 5d + 11f)?

To find the ratio $(3a+5c+11e):(3b+5d+11f)$, we can use the properties of ratios.

We are given the following ratios:
$\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{5}{7}$

Let each of these ratios be equal to a constant variable $k$:
$\frac{a}{b}=k$, which gives $a=bk$
$\frac{c}{d}=k$, which gives $c=dk$
$\frac{e}{f}=k$, which gives $e=fk$

Here, the value of $k$ is given as:
$k=\frac{5}{7}$

Now, let's substitute the expressions for $a$, $c$, and $e$ into the required ratio expression:
$\frac{3a+5c+11e}{3b+5d+11f}=\frac{3\left(bk\right)+5\left(dk\right)+11\left(fk\right)}{3b+5d+11f}$

We can factor out $k$ from the numerator:
$\frac{k(3b+5d+11f)}{3b+5d+11f}$

Canceling out the common term $(3b+5d+11f)$ from both the numerator and the denominator, we get:
$=k$

Since $k=\frac{5}{7}$, the ratio is:
$\frac{5}{7}$

Thus, the ratio is 5 : 7.