Average acceleration

$$ = {{change\,\,in\,\,velocioty} \over {time\,\,{\mathop{\rm int}} erval}}$$

$$ = {{\Delta \overrightarrow v } \over t}$$

$${\overrightarrow v _1} = +5\widehat i$$, towards east direction.

$$\overrightarrow {{v_2}} = +5\widehat j$$, towards north direction

$$\Delta \overrightarrow v = \overrightarrow {{v_2}} - \overrightarrow {{v_1}} $$ = $$5\widehat i - 5\widehat j$$

$$\therefore$$ $$\,\,\,\,\overrightarrow a = {{5\widehat j - 5\widehat i} \over {10}} = {{\widehat j - \widehat i} \over 2}$$

$$\therefore$$ $$\,\,\,\, a = {{\sqrt {{1^2} + {{\left( { - 1} \right)}^2}} } \over 2} = {{\sqrt 2 } \over 2} = {1 \over {\sqrt 2 }}m{s^{ - 2}}$$

$$\tan \theta = {{{v_2}} \over {{v_1}}} = {5 \over 5} = 1$$

$$\therefore$$ $$\,\,\,\,\theta = {45^ \circ }$$

Therefore the direction is North-west.