Rearrange:
3x+5=√(3-x),
9x2+30x+25=3-x,
9x2+31x+22=0=(x+1)(9x+22).
So x=-1 or -22/9. But these have to be tested in the original equation.
x=-1⇒ -3+5=2; √(3+1)=2. OK
x=-22/9⇒-66/9+5=-7/3; √(3+22/9)=7/3. Reject because √(3-x) implies the positive square root.
SOLUTION: x=-1