Translating words into math, we have the equations \begin{align*} a+b+c&=88\\ a-5&=N\\ b+5&=N\\ 5c&=N\\ \end{align*} We will express the value of each of $ a $, $ b $, and $ c $ in terms of $ N $ and then substitute these equations into the first given equation to solve for $ N $. From the second given equation, we have $ a=N+5 $. From the third given equation, we have $ b=N-5 $. From the fourth given equation, we have $ c=N/5 $. Plugging these equations into the first given equation to eliminate $ a $, $ b $, and $ c $, we have $ (N+5)+(N-5)+(N/5)=88\Rightarrow N=\boxed{40} $.