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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)137}\\\end{array}
Use the 1^{st} digit 1 from dividend 137
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)137}\\\end{array}
Since 1 is less than 25, use the next digit 3 from dividend 137 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)137}\\\end{array}
Use the 2^{nd} digit 3 from dividend 137
\begin{array}{l}\phantom{25)}00\phantom{4}\\25\overline{)137}\\\end{array}
Since 13 is less than 25, use the next digit 7 from dividend 137 and add 0 to the quotient
\begin{array}{l}\phantom{25)}00\phantom{5}\\25\overline{)137}\\\end{array}
Use the 3^{rd} digit 7 from dividend 137
\begin{array}{l}\phantom{25)}005\phantom{6}\\25\overline{)137}\\\phantom{25)}\underline{\phantom{}125\phantom{}}\\\phantom{25)9}12\\\end{array}
Find closest multiple of 25 to 137. We see that 5 \times 25 = 125 is the nearest. Now subtract 125 from 137 to get reminder 12. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }12
Since 12 is less than 25, stop the division. The reminder is 12. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.