ANSWER
[tex] 10C_5(2)^{5}( - 3)^5[/tex]
EXPLANATION
The given binomial expression is
[tex](2x-3y)^{10} [/tex]
The nth term in this expansion is calculated using the formula,
[tex]T_{r+1} = nC_ra^{n-r}b^r[/tex]
To find the term with coefficient
[tex] {x}^{5} {y}^{5} [/tex]
we substitute r=5, n=10, a=2x, and b=-3y
[tex]T_{6} = 10C_5(2x)^{10-5}( - 3y)^5[/tex]
[tex]T_{6} = 10C_5(2x)^{5}( - 3y)^5[/tex]
[tex]T_{6} = 10C_5(2)^{5}( - 3)^5 {x}^{5} {y}^{5} [/tex]
The coefficient is
[tex] 10C_5(2)^{5}( - 3)^5[/tex]
The second choice is correct.
