For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m) of the waves are :

Distance between crests  $=n\lambda =5$
So  $\lambda =\frac{5}{n}m\mathrm{........}\left(1\right)$
Also distance between a crest and trough is given as 1.5 m 

$\Rightarrow \left(2k-1\right)\frac{\lambda }{2}=1.5$ 
So  $\lambda =\frac{3}{2k-1}\mathrm{.......}\left(2\right)$
$\left(1\right),\left(2\right)$  satisfy, $\frac{n}{2k-1}=\frac{5}{3}=\frac{15}{9}=\frac{25}{15}$
 $\Rightarrow n\in \left\{5,15,25,\mathrm{.......}\right\}$
So  $\lambda \in \left\{1,\frac{1}{3},\frac{1}{5},\mathrm{........}\right\}$