`Answer:`
\(f\left(x\right)=5x-3x^2+2x^4-3x-x^4-5\)
\(=\left(2x^4-x^4\right)-3x^2+\left(5x-3x\right)-5\)
\(=x^4-3x^2+2x-5\)
\(g\left(x\right)=-2x^3+10x-1-7x^2+x^4-15x+10x^2\)
\(=x^4-2x^3+\left(-7x^2+10x^2\right)+\left(10x-15x\right)-1\)
\(=x^4-2x^3+3x^2-5x-1\)
\(f\left(x\right)+g\left(x\right)=\left(x^4-3x^2+2x-5\right)+\left(x^4-2x^3+3x^2-5x-1\right)\)
\(=\left(x^4+x^4\right)-2x^3+\left(-3x^2+3x^2\right)+\left(2x-5x\right)+\left(-5-1\right)\)
\(=2x^4-2x^3-3x-6\)