The remainder on dividing $5^{99}$ by 11 is_______________
$5^{99}=5^{4} .5^{95}$
$=625[5^{5}]^{19}$
$=625[3125]^{19}$
$=625[3124+1]^{19}$
$=625[11 k \times 19+1]$
$=625 \times 11 k \times 19+625$
$=11 k_1+616+9$
$=11(k_2)+9$
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