x = Range[0.001, 1000];
y = 5 - Log[x];
ListPlot[Transpose[{x, y}], PlotRange -> All]
ListLogLinearPlot[Transpose[{x, y}], PlotRange -> All]

x = Range[0.001, 1000];
y = 5 - Log[x];
pl = ListLogLinearPlot[Transpose[{x, y}], PlotRange -> All];
PlotRange /. Options[pl, PlotRange]
plotRange[Show[pl, PlotRange -> All, PlotRangePadding -> 0]]

{{-7.19556, 6.90676}, {-1.90676, 11.9078}}
{{-7.41591, 6.90676}, {-1.90676, 11.9078}}

x = Range[0.001, 1000];
y = 5 - Log[x];
pl = ListLogLinearPlot[Transpose[{x, y}], PlotRange -> All,
   Frame -> True, Axes -> False];
Options[pl, PlotRange]

pl2 = Show[pl, PlotRange -> All]

plotRange[pl2]

{{-6.90776, 6.90676}, {-1.90676, 11.9078}}

ListLogLinearPlot[Transpose[{x, y}], PlotRange -> All, Frame -> True
  ] // {#, Cases[#, Point[x_] :> E^x[[1, 1]], ∞]} &

ListLogLinearPlot[Transpose[{x, y}], PlotRange -> Full, Frame -> True]

x = Range[0.001, 1000];
y = 5 - Log[x];
ListLogLinearPlot[Transpose[{x, y}],
  PlotRange -> All, PlotRangePadding -> {{10., .1}, Automatic}]