Schematic diagram for motion of body is
Average speed $=\frac{\text { Total displacement }}{\text { Total time }}$
In interval $t=0$ to $t=10 \mathrm{~s}$;
Displacement, $s_1=\frac{1}{2} a_1 t^2=\frac{1}{2} \times 5 \times(10)^2=250 \mathrm{~m}$
Final velocity, $v_1=u+a_1 t$
$\Rightarrow \quad v_1=0+5 \times 10=50 \mathrm{~ms}^{-1}$
In interval $t=10 \mathrm{~s}$ to $t=15 \mathrm{~s}$,
$v_1=50 \mathrm{~ms}^{-1}, v_2=0 \mathrm{~ms}^{-1}, t=5 \mathrm{~s}$
Using
$$
v=u+a t
$$

We have, $\quad a_2=\frac{0-50}{5}=-10 \mathrm{~ms}^{-2}$
And by $v^2-u^2=2 a s$, we have
$$
v_2^2-v_1^2=2\left(a_2\right) s_2 \Rightarrow s_2=\frac{50 \times 50}{2 \times 10}=125 \mathrm{~m}
$$

So, average speed for interval, $t=0$ to $t=15 \mathrm{~s}$, we have
$$
v_{\mathrm{avg}}=\frac{s_1+s_2}{t_1+t_2}=\frac{250+125}{10+5}=\frac{375}{15}=25 \mathrm{~ms}^{-1}
$$