Which molecule ${\mathrm{AX}}_3,{\mathrm{AX}}_4,{\mathrm{AX}}_5,{\mathrm{AX}}_6$ is most likely to have a trigonal bipyramidal structure if A has no lone pair? 

Trigonal bipyramidal geometry corresponds to${\mathrm{sp}}_3\mathrm{d}$ hybridization with 5 bond pars and no lone pairs
⇒ For which there must be 5 monovalent atoms.

  $\therefore { \mathrm{AX}}_5$ is most likely to have a trigonal bipyramidal structure if A has no lone pair.

Hence, the option B is correct.