If you don't know anything other than observations are independent, then you could use negative exponential. Since this is memoryless, you can also use it for the first observation.
If you know the min and max values then you could try to approximate a shape by reverting to triangular or looking for a distribution by matching shape visually.
What do you mean by the same? If you decide to use that for both they will of course be the same type but each will have a different parameter since the means are different (5mins and 20 mins).
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