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Translating words into math, we have the equations $$\begin{array}{rl}a+b+c& =88\\ a-5& =N\\ b+5& =N\\ 5c& =N\end{array}$$ 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 $(N+5)+(N-5)+(N/5)=88\Rightarrow N=\boxed{40}$.