Calculus of a Single Variable, Chapter 3, 3.5, Section 3.5, Problem 17c

You need to evaluate the limit, hence, you need to replace oo for x in equation:
lim_(x->oo) (5 - 2x^(3/2))/(3x -4) = (5 - oo)/(3oo - 4) = -(oo)/oo
Since the result is indeterminate, you need to force x^(3/2) and x factors out at numerator and denominator:
lim_(x->oo) (x^(3/2))(5/(x^(3/2)) - 2)/(x(3 - 4/x)
Since lim_(x->oo) 5/(x^(3/2)) = 0 and lim_(x->oo)4/x = 0, yields:
lim_(x->oo) (x^(3/2 - 1))(-2/3) = -2/3*lim_(x->oo) (x^(1/2)) = -2/3*oo = -oo
Hence, evaluating the given limit yields lim_(x->oo) (5 - 2x^(3/2))/(3x -4) = -oo.