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Set $x$ as the original number.

Write out equations: 

$\frac {x-5} {4} = \frac {x-4} {5}$

Cross-multiply:

$(x-5)5=(x-4)4$

Simplify to...

$5x-25=4x-16$

Solve the equation by subtracting $4x$ from both sides:

$x-25=-16$

Then add $25$ on both sides:

$x=-16+25=9$

So the final answer would be $x=9$

we would make the equation (x-5)/4=(x-4)/5 and simplify it into 5x-25=4x-16 when we multiply both sides by 20 and subtract 4x from both sides to get x-25=-16 we then add 16 from both side to get x-9=0 and then we finnaly add 9 to both sides to get x=9