A=(({{0.3132, 0.3566, 0.2545, 0.2579, 0.2063}, {-0.0897, 0.2913, 0.1888, 0.4392, 0.1970}, {0.0845, 0.2433, -0.5888, -0.0407, 0.1749}, {0.2478, -0.1875, 0.2233, 0.3126, -0.6711}, {0.1744, 0.2315, -0.1004, -0.2111, 0.0428}}));

x(0) tž. ||x(0)||=1 ? max/min||x(3)||?

{U,Σ,V}=SingularValueDecomposition@A

{{{-0.004114645630179765`,-0.7282661873283564`,0.2506046622544516`,0.42439915915113957`,-0.47612402486505`},{-0.010849012483216236`,-0.6807648110177981`,-0.18121700604688312`,-0.5222465828375408`,0.48047942145523376`},{0.5509642334777703`,0.0591748808697323`,0.6655580532496418`,-0.4717851094912405`,-0.1654933083819107`},{-0.8038615544824161`,0.04810036819895048`,0.5631145348310465`,-0.1667881853112314`,0.0810967182248379`},{0.22385348617531817`,-0.019295609016012225`,0.37985812929605134`,0.5447424823980976`,0.7130783446987577`}},{{0.9607491824999831`,0.`,0.`,0.`,0.`},{0.`,0.8128530186923959`,0.`,0.`,0.`},{0.`,0.`,0.5393583559955016`,0.`,0.`},{0.`,0.`,0.`,0.3879276056911143`,0.`},{0.`,0.`,0.`,0.`,0.12023549762387797`}},{{-0.11856988290960657`,-0.18880900769616663`,0.6614734650434055`,0.4989963775325968`,-0.5135638341359396`},{0.34553047517383984`,-0.5623341555586407`,0.33532541527333126`,0.10776666120483562`,0.6635753166165993`},{-0.5511119825172037`,-0.41340342197149005`,-0.5093269501643262`,0.503342772608423`,0.11227334735987354`},{-0.34014381329542853`,-0.5783464948637015`,0.0997366082645967`,-0.6904629186319857`,-0.2512590000811696`},{0.6686760371029787`,-0.3778152970514447`,-0.42502751407811057`,0.09641562735974521`,-0.46923725107411546`}}}

fn[t_]:=U.MatrixExp[Σ*t].Transpose[V]

g1=Plot[(fn[t].{1,0,0,0,0})[[1]],{t,0,3},PlotStyle->{Dashed,Red}];
g2=Plot[(fn[t].{0,0,0,0,1})[[1]],{t,0,3},PlotStyle->{Dashed,Blue}];
Show[g1,g2]

Σ//MatrixForm