Question 1082221
Yes it's possible. I was able to construct it with <a href = "https://www.geogebra.org/home?ggbLang=en">GeoGebra</a> (free graphing software). 
The drawing is to scale. 
<img src = "https://i.imgur.com/GLPLcNT.png">
This is not the only way to form a pentagon with these side lengths. There are other possibilities. Such as this
<img src = "https://i.imgur.com/OyECUiI.png">
And many others as well.