There is a rule that specifies whether or not the triangle exist. 
Rule: When added, the two smaller sides of the triangle must be greater than the longest side. 
In this case answer C fits the choice. 
Since the small sides are 8cm and 15cm 
8 + 15 = 23 
And the biggest side of the triangle is 22 
23 > 22 
Answer = C. 8cm, 5cm, 10cm