If a single bacteriophage infects one e. coli cell present on a lawn of bacteria and, upon lysis, yields 325 viable viruses, how many phages will exist in a single plaque if 5 more lytic cycles occur?

The answer is 3,625,908,203,125. This calculated by (325)^5  .

This is exponential growth where the population of the virus doubles in every lytic cycle and decimates the E. coli population. In some hours the lawn of E. coli cells will be completely mowed down. The other life cycle  of bacteriophages, other than lytic, is lysogenic cycle that does not lyse the bacteria but only integrates its DNA in the genome and is replicated when the bacteria divides.

it takes hundreds of years to become stable.

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