Create some data:
object = RandomReal[{0, 5}, {10, 5}];
Grid @ Partition[ListPlot[#, Joined -> True, PlotRange -> 5] & /@ object, 2]
(* or in a more textbook-style: *)
Grid[Partition[Table[ListPlot[object[[i]], Joined -> True, PlotRange -> 5], {i, 1, Length[object]}], 2]]

and a desired
object:
desired = RandomReal[{0, 5}, 5];
ListPlot[desired, Joined -> True, PlotRange -> 5]

According to the description: "minimal sum of differences between the corresponding values", compute
s = Total /@ (Abs @ Subtract[desired, #] & /@ object)
(* textbook-style: *)
s = Table[Total[Abs[desired - object[[i]]]], {i, 1, Length[object]}]
{8.60733, 6.7376, 8.20597, 5.4877, 9.9549, 10.0675, 8.00134, 10.2252,
10.2552, 13.7893}
Position[s, Min @ s] (* or: Position[s, Min[s]] *)
{{4}}
i.e., the fourth object is the closest to the desired one.
For a more general approach, see Nearest
.
Nearest
. $\endgroup$ – corey979 Nov 15 '16 at 23:47