5. To some natural number, two two-digit numbers were appended sequentially to the right. The resulting number turned out to be equal to the cube of the sum of the three original numbers. Find all possible triples of the original numbers.
5. Let $a$ denote the first natural number, and $b$ and $c$ the two-digit numbers written after it. Let $x=a+b+c$. According to the condition, the numbers $a, b, c$ and $x$ satisfy the equation $10^{4} a+100 b+c=x^{3}$ (see fact 11). Therefore,

$$
x^{3}=10^{4} a+100 b+c44$;
2) $x=45(x-1=44), 45^{3}=91125, a=9, b=11, c=25$;
3) $x=54(x+1=55), 54^{3}=157464,15+74+64>54$;
4) $x=55(x-1=54), 55^{3}=166375,16+63+75>55$;
5) $x=89(x-1=88, x+1=90), 89^{3}=704969,70+49+$ $+69>89$
6) $x=98(x+1=99), 98^{3}=941192,94+11+92>98$;
7) $x=99,99^{3}=970299,97+2+99>99,2-$ is not a two-digit number.