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Choice B is correct. The given expression may be rewritten as $x^2+8x-5x-40$. Since the first two terms of this expression have a common factor of $x$ and the last two terms of this expression have a common factor of $-5$, this expression may be rewritten as $x\left(x\right)+x\left(8\right)-5\left(x\right)-5\left(8\right)$, or $x\left(x+8\right)-5\left(x+8\right)$. Since each term of this expression has a common factor of $\left(x+8\right)$, it may be rewritten as $\left(x-5\right)\left(x+8\right)$.

Alternate approach: An expression of the form $x^2+bx+c$, where $b$ and $c$ are constants, can be factored if there are two values that add to give $b$ and multiply to give $c$. In the given expression, $b=3$ and $c=-40$. The values of $-5$ and $8$ add to give $3$ and multiply to give $-40$, so the expression can be factored as $\left(x-5\right)\left(x+8\right)$.

Choice A is incorrect. This expression is equivalent to $x^2+6x-40$, not $x^2+3x-40$.

Choice C is incorrect. This expression is equivalent to $x^2-3x-40$, not $x^2+3x-40$.

Choice D is incorrect. This expression is equivalent to $x^2-6x-40$, not $x^2+3x-40$.