Plot1=ListPlot[{{0,0},{1,0.5},{2,3},{2.5,2},{3,5}}]

n=2;
coeffA=Table[(Subscript[a, i]),{i,0,n}];
coeffB=Table[(Subscript[b, i]),{i,1,n}];
cosA=Table[Cos[k*x],{k,0,n}];
sinB=Table[Sin[k*x],{k,1,n}];
trigPoly[x_]=coeffA.cosA+coeffB.sinB

t=2Pi/3.5*x;
2Pi/3.5*0
2Pi/3.5*1
2Pi/3.5*2
2Pi/3.5*2.5
2Pi/3.5*3

r=NSolve[{trigPoly[0]==0,trigPoly[1.7952]==0.5,trigPoly[3.59039]==3, trigPoly[4.48799]==2,trigPoly[5.38559]==5}]

z=trigPoly[x]/.r

Plot2=Plot[z,{x,0,5}]

Show[{Plot1,Plot2}]