Answer
$6x-13\sqrt{x}-5$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL method, then,
\begin{array}{l}
\left( 2\sqrt{x}-5 \right)\left( 3\sqrt{x}+1 \right)
\\=
(2\sqrt{x})(3\sqrt{x})+(2\sqrt{x})(1)+(-5)(3\sqrt{x})+(-5)(1)
\\=
6\sqrt{x^2}+2\sqrt{x}-15\sqrt{x}-5
\\=
6x-13\sqrt{x}-5
.\end{array}