In[]:=
Select[Tuples[Range[50],4],5(#[[1]]+#[[2]]+#[[3]]+#[[4]])+10==2*#[[1]]*#[[2]]*#[[3]]*#[[4]]&&#[[1]]<=#[[2]]<=#[[3]]<=#[[4]]&]
Out[]=
{{1,1,3,35},{1,1,5,9}}