The honest answer
A single summon keeps the listed odds. A 3★ streak does not make the next pull more likely to be 5★, and a 10x summon usually does not secretly improve the 5★ rate.
What you can improve is your overall chance across multiple pulls, your portal choice, and your gem efficiency.
What actually helps
Choose by target
If you want any 5★, compare the total Legendary rate. If you want one specific featured hero, the featured rate matters much more.
Plan the number of pulls
More pulls increase your chance of at least one hit, but never create a guarantee. At 2.5%, even 30 pulls can miss.
Count bonus draws separately
HOTM and Secret Summon chances are separate bonus rolls. They should not be mixed into the normal 5★ pool.
Use gem discounts
Single, 10x, and 30x options usually share the same pull odds. Their main difference is cost and portal-specific bonus progress.
Common summon myths
Practical rule
Do not ask “Can I get lucky?” You can always get lucky. Ask: “Am I comfortable with the chance of getting nothing useful after this many pulls?”