It looks like you're presenting a sequence of fractions and might be asking to determine the next number in the sequence. To solve this, let's first observe the given fractions:

1. $-\frac{2}{3}$
2. $\frac{1}{15}$
3. $\frac{5}{9}$
4. $\frac{19}{21}$
5. $\frac{7}{6}$

Step 1: Identify the Pattern

Let's see if there is a common difference or ratio between consecutive terms, or if the numerators and denominators follow a particular rule.

Analyzing the Numerators and Denominators Separately:

Numerators:

• The numerators are: $-2, 1, 5, 19, 7$

At first glance, there is no obvious arithmetic or geometric progression in the numerators.

Denominators:

• The denominators are: $3, 15, 9, 21, 6$

Similarly, the denominators do not seem to follow a straightforward arithmetic or geometric pattern.

Step 2: Look for Other Types of Patterns

We can try to observe other relationships, such as a pattern involving alternating signs, ratios, or some recursive relationship. However, the signs don't alternate consistently, and no clear multiplicative or additive rule is evident.

Conclusion

The sequence does not immediately conform to a standard arithmetic, geometric, or other common progression patterns. Therefore, additional information or context might be needed to identify the next term in this sequence.

Would you like to provide more context or specify if this is part of a particular type of mathematical problem?

Further Questions:

1. Do you know if the sequence follows a specific type of mathematical pattern?
2. Are there any other sequences or series that resemble this one?
3. Could the sequence be generated by a mathematical formula or function?
4. Are there any constraints or rules you can provide that apply to this sequence?
5. Is the sequence part of a larger mathematical puzzle or challenge?

Tip: When trying to find the next term in a sequence, always look for patterns in both numerators and denominators separately. If no standard patterns are found, consider looking for non-linear or more complex relationships.