A dish holds 150 bacteria. Each bacterium divides into two every 25 minutes, and none dies…

Step 1. Divisions in 5 hours. $5\ \text{h} = 300\ \text{min}$, and $\dfrac{300\ \text{min}}{25\ \text{min}} = 12$ divisions.

Step 2. The number. $150 \times 2^{12} = 150 \times 4096 = 614\,400$ bacteria.

Step 3. Past a million. After $12$ divisions there are $614\,400$, which is too few. After $13$ there are $1\,228\,800$.