#### Answer

$(-5,-\frac{1}{3})$

#### Work Step by Step

$3x^2+16x\lt-5$ Write as an equation.
$3x^2+16x+5=0$ Factor by grouping.
$(3x+1)(x+5)=0$ Solve as an equation.
$x=-5$
$x=-\frac{1}{3}$
Plot these numbers on a number line,split them into intervals, take one test point from each interval, and check them to see if they are true. If they are true, then it is a solution.
In this case, it is
$(-5,-\frac{1}{3})$