The length of the portion of the straight line $5x+12y=60$ intercepted between the axes is:

The correct option is 13.

We are given the equation of the straight line:

$5x+12y=60$

To find the intercepts made by the straight line on the coordinate axes, we can convert the equation into the intercept form $\frac{x}{a}+\frac{y}{b}=1$, where $a$ is the x-intercept and $b$ is the y-intercept.

Dividing both sides of the equation by 60:

$\frac{5x}{60}+\frac{12y}{60}=\frac{60}{60}$

$\frac{x}{12}+\frac{y}{5}=1$

From this form, we can identify:

The x-intercept point on the x-axis is $A(12,0)$, so the x-intercept length is $a=12$.
The y-intercept point on the y-axis is $B(0,5)$, so the y-intercept length is $b=5$.

The portion of the straight line intercepted between the coordinate axes is the segment joining point $A(12,0)$ and point $B(0,5)$.

Using the distance formula $d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$:

$AB=\sqrt{{(12-0)}^2+{(0-5)}^2}$

$AB=\sqrt{{12}^2+{(-5)}^2}$

$AB=\sqrt{144+25}$

$AB=\sqrt{169}$

$AB=13$

Thus, the length of the portion of the straight line intercepted between the axes is 13.