Hey there! I'm happy to help!
Let's call our fraction x.
x=5.2727272727......
We want to get rid of the repeating decimals. If we multiply our fraction by 100, we have that 100x=527.27272727.....
100x=527.2727272727....
x=5.27272727....
If we subtract these equations, the repeating stuff will be gone and we can solve for x.
99x=522
We divide both sides by 99.
x=522/99= 58/11= 5 3/11.
Have a wonderful day! :D