Writing:

    points = {{5.667680905429296, 4.978997738176498}, 
              {6.062672641119444, 4.821312039084925}, 
              {6.463307024854181, 4.616923216296398}, 
              {6.869389071217502, 4.358024801663491}, 
              {7.280737790273085, 4.0328205724875374}, 
              {7.697184816760531, 3.6220668338026347}, 
              {8.118573184417112, 3.090204786097973}, 
              {8.544756235833926, 2.354492374103027}, 
              {8.97559665513716, 1.045159976700232}, 
              {9.168625618559851, 6.355895552341976^-16}, 
              {9.291801857401657, 6.34776334121662^-20}};

    f = Interpolation[points];

    Plot[f[x], {x, points[[1, 1]], points[[11, 1]]}, 
               Epilog -> Point[points], 
               AxesLabel -> {x, y}]

I get:

[![enter image description here][1]][1]

which is what you want.

  [1]: https://i.sstatic.net/GFvzR.png