We have
135₁₀ = 1×10² + 3×10¹ + 5×10⁰
but since 10 = 2×5, we can write
135₁₀ = 1×(2×5)² + 3×(2×5)¹ + 5×(2×5)⁰
135₁₀ = 4×5² + 6×5¹ + 5×5⁰
135₁₀ = 4×5² + 6×5¹ + 1×5¹
135₁₀ = 4×5² + 7×5¹
135₁₀ = 4×5² + (5 + 2)×5¹
135₁₀ = 4×5² + 5×5¹ + 2×5¹
135₁₀ = 4×5² + 1×5² + 2×5¹
135₁₀ = 5×5² + 2×5¹
135₁₀ = 1×5³ + 2×5¹
135₁₀ = 1020₅
A possibly faster method: we have 5³ = 125 < 135 < 525 = 5⁴. Now,
135 = 125 + 10 = 5³ + 2×5
which agrees with the first method, 135₁₀ = 1020₅.