Solution
If the expression is divisible by x-1 then x = 1 is a root of the expression.
Substituting value of x in the expression :
$$4\cdot1^2+k\cdot1+5\ =\ 0$$
==> k = -9.
The expression can be written as:
$$4x^2-9x+5$$
==> $$4x^2-4x-5x+5\ =4x\left(x-1\right)-5\left(x-1\right)=\left(x-1\right)\left(4x-5\right)$$
The expression is also divisible by 4x-5
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