Where Im@qpC32 != 0 do qpC32=0 && Plot[Re@qpC32, {q, 0, 2000}, {m5, 0, 2000}]
Where Im@qpC34 != 0 do qpC34=0 && Plot[Re@qpC34, {q, 0, 2000}, {m5, 0, 2000}]

Plot[Re@qpC32+Re@qpC34, {q, 0, 2000}, {m5, 0, 2000}]

eqn = j -
    Sqrt[q^2 + qp^2 -
      2 q qp Cos[[Theta]]] - [Sqrt](qp^2 +
       1/2 (16 m5^2 + ma^2 + mp^2 -
          Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
            4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0;
With[{gensol = Solve[eqn , qp]},
  Block[{[Theta] = Pi/12, m = 5.5, M = 300, Nc = 3, c = !(*
TagBox[
InterpretationBox[
RowBox[{""<-4.46874>"", "*",
SuperscriptBox["10", ""<4>""]}],
-44687.3983417778,
AutoDelete->True],
ScientificForm]), b = !(*
TagBox[
InterpretationBox[
RowBox[{""<1.61594>"", "*",
SuperscriptBox["10", ""<5>""]}],
161593.81818181818`,
AutoDelete->True],
ScientificForm]), k1 = !(*
TagBox[
InterpretationBox[
RowBox[{""<1.6485>"", "*",
SuperscriptBox["10", ""<1>""]}],
16.485010961790245`,
AutoDelete->True],
ScientificForm]), k2 = !(*
TagBox[
InterpretationBox[
RowBox[{""<-1.31313>"", "*",
SuperscriptBox["10", ""<1>""]}],
-13.131344420001051`,
AutoDelete->True],
ScientificForm]), ma, mp,
    j},(*subs vals when gensol is evaluated*){j = [Sqrt](q^2 +
        1/2 (16 m5^2 + ma^2 + mp^2 +
           Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 -
             4 (ma^2 mp^2 - 16 m5^2 q^2)])),
    ma = [Sqrt](-2 (M^2 -
          2 (3 k1 + k2) (Sqrt[(c + M^2 + 2 m5^2)/(2 (k1 + k2))] +
             m b/(2 (c + M^2 + 2 m5^2)))^2 - c + 2 m5^2)),
    mp = Sqrt[
     2 b m (Sqrt[(c + M^2 + 2 m5^2)/(2 (k1 + k2))] +
        m b/(2 (c + M^2 + 2 m5^2)))^-1]};
   sols = gensol]];
qpC32 = Compile[{{q, _Complex}, {m5, _Complex}},
   Evaluate[qp /. sols[[2]]],
   RuntimeOptions -> "EvaluateSymbolically" -> False] ;
qpC34 = Compile[{{q, _Complex}, {m5, _Complex}},
   Evaluate[qp /. sols[[4]]],
   RuntimeOptions -> "EvaluateSymbolically" -> False] ;
Plot3D[ Re@qpC34[q, m5], {q, 0, 2000}, {m5, 0, 2000},
 PlotRange -> Full]
Plot3D[ Im@qpC34[q, m5], {q, 0, 2000}, {m5, 0, 2000},
 PlotRange -> Full]
Plot3D[ Re@qpC32[q, m5], {q, 0, 2000}, {m5, 0, 2000},
 PlotRange -> Full]
Plot3D[ Im@qpC32[q, m5], {q, 0, 2000}, {m5, 0, 2000},
 PlotRange -> Full]

rg32 = Function[{q, m5}, Chop[Im[qpC32[q, m5]]] == 0];
rg34 = Function[{q, m5}, Chop[Im[qpC34[q, m5]]] == 0];
plt32 = Plot3D[Re@qpC32[q, m5], {q, 0, 2000}, {m5, 0, 2000}, RegionFunction -> rg32];
plt34 = Plot3D[Re@qpC34[q, m5], {q, 0, 2000}, {m5, 0, 2000}, RegionFunction -> rg34];