In YDSE, path difference, $\Delta \text{x}=\text{d sin}\theta$

For maxima, $\Delta \text{x}=\text{n}\lambda$, where $\text{n}=0\text{, }\pm 1\text{, }\pm 2\text{....}$

$\frac{5\lambda }{2}\text{sin}\theta =\text{n}\lambda$  (given that $\text{d}=\frac{5\lambda }{2}$)

$\begin{array}{l}\Rightarrow \sin \theta =\frac{2n}{5} ...\left(i\right)\end{array}$

Since, −1≤sinθ≤1 From (i) ⇒−1≤ 2n/5 ≤1
$$

So, $-\frac{5}{2}\le \text{n}\le \frac{5}{2}$

So, possible values of n are -2, -1, 0, 1, 2 Thus a total of 5 maximas will be obtained.