If a function f(x), g(x), h(x), etc., has no x's on the
right side, it is a CONSTANT FUNCTION.

Examples:  f(x) = 5,  g(x) = -3, h(x) = 0 are all CONSTANT functions:

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If a function f(x), g(x), h(x), etc., has 1 understood 
as its largest power of x on the right side, it is a 
LINEAR FUNCTION.

Examples:  f(x) = x,  g(x) = -4x+7, h(x) = 7-5x are all LINEAR functions:

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If a function f(x), g(x), h(x), etc., has 2 as its largest 
power of x on the right side, it is a QUADRATIC FUNCTION.

Examples:  f(x) = 4x² - 3x + 7,  g(x) = -x², h(x) = 9-6x² are 
all QUADRATIC functions:

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If a function f(x), g(x), h(x), etc., has 3 as its largest 
power of x on the right side, it is a CUBIC FUNCTION.

Examples:  f(x) = -3x³ - 8x² + 7x + 6,  
g(x) = x³, h(x) = 9x² - 7x³ are all CUBIC functions:

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If a function f(x), g(x), h(x), etc., has 4 as its largest 
power of x on the right side, it is a QUARTIC FUNCTION.

Examples:  f(x) = -7x4 - 9x³ + 7x² + 6x - 4,  
g(x) = -x4, h(x) = 6x² - 7x4 are all 
QUARTIC functions:

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So your function g(x) = -5x4 - 6

is a QUARTIC function.

The degree is 4, the largest exponent of x.

The leading coefficient is the coefficient of the term
with the largest power of x, which in this case is -5

Edwin