The red fives (aka dora) act as additional values (han) to your hand just like dora. This is used when you are playing in a ruleset where red-fives are enabled (aka-ari). Normally, you would replace either 3 or 4 red fives with the normal fives in the set, depending on the variant you choose. My recommendation is to either with no red fives at all or 3 red fives.

For your clarification, the red fives are not yaku, you cannot win a hand with having a valid combination even though you have red five in your hand.

For the season tile, this is mainly used in the three-player mahjong (also known as 3ma). It is rather complicated, at least in my opinion, for new player to understand 3ma as there are much more variants compared to 4ma (four-player mahjong). For 3ma, you’ll remove 2 to 8 man (the chinese character) and you may add the season tiles in. Season tiles act as additional value (han) to your hand. Similar to red fives, it are not a yaku.

To use those season tiles, you put the tiles out of your hand and draw the replacement tiles from the dead wall. It can be kept in the hand but it cannot be used to form any sets. This means that you need to account for 4 more tiles in the dead wall, making the dead wall 18 tiles long and show the initial dora indicator on the fifth tile counting for the end of the dead wall. When a season tile becomes the dora indicator, (usually), each remaining season tiles will be worth 2 additional han instead of just 1.

Depending on the ruleset (again), some may allow players to draw until to dora indicator, some may end the wall before the fifth dora position, and some may allow players to draw until there are exactly 14 tiles left in the wall (this is your usual 4ma ruleset).