What is the next term in the series: 5,14,19,? and how?

A big part of math is pattern recognition. A lot of homework is just fighting with stuff so you will remember the pattern when you see it again. A series is either adding, multiplying, or a power, sometimes more complex. So you look at the given figures and you see steps of 5, 9, and 5. That is not adding, so it is not an aritmetic sequence. It does not appear to be powers either. So we examine multiplication.

n x(n)
1 5 ... 5 times n
2 14 .. 5 times n = 10
3 19 .. 5 times n = 15

Let's try another pattern.
1 .. 5n + 4 = 9
2 .. 5n + 4 = 14
3 .. 5n + 4 = 19

I don't think there is a sequence there.

Often there is a surprise in this field. About forty years ago, Games Magazine offered a series which turned out to be ten digits in alphabetic order. About eight months later a reader submitted a mathematical process that generated that exact order.