Question 973896

Let the three consecutive numbers be {{{x}}}, {{{(x+1)}}}, {{{(x+2)}}}

if the product two integers is {{{5}}} less than {{{5}}} times the largest integer, then we have

{{{x(x+1)+5=5(x+2)}}}

{{{x^2+x+5=5x+10}}}

{{{x^2+x+5-5x-10=0}}}

{{{x^2-4x-5=0}}}....factor 

{{{x^2+x-5x-5=0}}}

{{{(x^2+x)-(5x+5)=0}}}

{{{x(x+1)-5(x+1)=0}}}

{{{(x-5)(x+1)=0}}}

solutions:

if {{{(x-5)=0}}}=>{{{x=5}}}

if {{{(x+1)=0}}}=>{{{x=-1}}}

so, since your integers are positive, disregard {{{x=-1}}}

your solution is: 
{{{x=5}}}
{{{(x+1)=6}}}
{{{(x+2)=7}}}