In[]:=
FindInstance[5(a+b+c+d)+10==2*a*b*c*d,{a,b,c,d},PositiveIntegers,2]
FindInstance
:The methods available to FindInstance are insufficient to find the requested instances or prove they do not exist.
Out[]=
FindInstance[10+5(a+b+c+d)2abcd,{a,b,c,d},

>0
,2]
In[]:=
FindInstance[5(a+b+c+d)+10==2*a*b*c*d,{a,b,c,d},PositiveIntegers]
Out[]=
{{a5,b9,c1,d1}}
In[]:=
FindInstance[{5(a+b+c+d)+10==2*a*b*c*d,a!=5,b!=5,c!=5,d!=5},{a,b,c,d},PositiveIntegers]
Out[]=
{{a1,b1,c3,d35}}