IfWhen you use a frame, axes are suppressed, so you need to give Axes -> True
. Also you must provide some extra space along the left side and bottom of the plot.
Plot[t^2, {t, 0, 5},
PlotStyle -> Blue,
Frame -> {{True, TrueFalse}, {True, FalseTrue}},,
PlotRangePadding -> {{.75, Automatic}, {5, Automatic}},
Axes -> True,
AxesLabel -> {"x label", "y label"}]