Answer:
![(1)/(4)](https://img.qammunity.org/2019/formulas/mathematics/college/uvah8srijoolvb1xwlyapdljmkw8sncji8.png)
Explanation:
The leading coefficient of a polynomial are the real numbers that is placed in front of the variable with the highest exponent.
Given polynomial function :
![f(x)=(1)/(4)x^5+8x-5x^4-19](https://img.qammunity.org/2019/formulas/mathematics/college/qrjjvmh8a9ey646u7gzy1nffg1gkgir1r4.png)
Variable with the highest exponent=
![x^5](https://img.qammunity.org/2019/formulas/mathematics/high-school/rmh3awc7rlvsip23fhkocr1jcutc05zmbw.png)
Number placed in front of
![x^5=(1)/(4)](https://img.qammunity.org/2019/formulas/mathematics/college/lllg87efhq2mapxzf69p7rgh8z7z28eq0k.png)
Hence, the leading coefficient =
![(1)/(4)](https://img.qammunity.org/2019/formulas/mathematics/college/uvah8srijoolvb1xwlyapdljmkw8sncji8.png)