Question 1200437
Follow the description exactly!
(Your description is slightly ambiguous.)


8 and 29



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If x is first number, then 5x-11 is second number.


The ambiguity is in the second part allowing confusion of "three times" what.
The part could be taken as  {{{3(x+5x-11)}}} to be equated to 53.
 Going with this, 

{{{3(x+5x-11)=53}}}
{{{3(6x-11)=53}}}
{{{18x-33=53}}}
{{{18x=53+33}}}
{{{18x=86}}}
{{{x=86/18=43/9}}}----------probably not what you want


Other interpretation might be better.
{{{3x+(5x-11)=53}}}
-
{{{8x-11=53}}}
{{{8x=64}}}
{{{highlight(x=8)}}}----------first number.
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{{{5x-11=5*8-11=40-11=highlight(29)}}}------second number.