The upper critical fields, $H_{c2}$($T$), of single crystals of the superconductor Ca$_{10}$(Pt$_{4-delta}$As$_{8}$)((Fe$_{0.97}$Pt$_{0.03}$)$_{2}$As$_{2}$)$_{5}$ ($delta$ $approx$ 0.246) are determined over a wide range of temperatures down to $T$ = 1.42 K and magnetic fields of up to $mu_{0}H$ $simeq$ 92 T. The measurements of anisotropic $H_{c2}$($T$) curves are performed in pulsed magnetic fields using radio-frequency contactless penetration depth measurements for magnetic field applied both parallel and perpendicular to the textbf{ab}-plane. Whereas a clear upward curvature in $H_{c2}^{paralleltextbf{c}}$($T$) along textbf{H}$parallel$textbf{c} is observed with decreasing temperature, the $H_{c2}^{paralleltextbf{ab}}$($T$) along textbf{H}$parallel$textbf{ab} shows a flattening at low temperatures. The rapid increase of the $H_{c2}^{paralleltextbf{c}}$($T$) at low temperatures suggests that the superconductivity can be described by two dominating bands. The anisotropy parameter, $gamma_{H}$ $equiv$ $H_{c2}^{paralleltextbf{ab}}/H_{c2}^{paralleltextbf{c}}$, is $sim$7 close to $T_{c}$ and decreases considerably to $sim$1 with decreasing temperature, showing rather weak anisotropy at low temperatures.
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