Sum Of Five Squares?

$2a^2 +3b^2 =35$ , so $|b| \leq \sqrt {\frac {35}{3}} < 4$ . Checking all values for $|b|$ , we get that $(|a|,|b|) =(4,1), (2,3)$ . For each such ordered pair, we have $4$ solutions (one in each quadrant ), so this makes $4 \times 2 =8$ solutions in all.