Ignore the other 3 suits. The responder has found the suit to play. The responder does not know what the opener has or does not have in addition to 5+spades. Do not be tempted by better looking suits. The opener may not be able to support other suits. Act on what is known, not on what is hoped for.

By rebidding spades, the responder is SUPPORTING the spades. The opener knows the responder has at least 3-spades and the partnership will play a spades contract. The level of the responder's next bid indicates the point count range of its hand, which will be used by the opener to find the appropriate contract level to play.

Support raises are not subject to the 1-over-1 restriction. If the responder has:
     6-9 pts:  Bid  2 ♠  - a single raise indicating the point count range. There are not enough combined partnership points for a game.
     10-12 pts:  Bid  3 ♠  - a double raise indicating the point count range. There are not quite enough combined partnership points for a game.
     13-16 pts:  Bid  4 ♠  - a triple raise to game. There are enough partnership points for a game in spades. The opener will consider this bid as a close-out bid, and will likely pass.
     17-20 pts:  Bid  3 NT  - jump-shift raise indicates the responder's spade support and point count range. This commits the partnership to a game level contract, and maybe more. This bid gives the opener the options to play the game level contract in No Trump, play the game level contract in 4-Spades, or explore a slam contract.

The #1 priority is to support the opener's spades. Support raises are not subject to the 1-over-1 restriction. If the responder has:
     6-9 pts:  responder has 2 options:
        • Bid  2 ♠  - a single raise indicating the point count range. There are not enough combined partnership points for a game.
        • Bid  4 ♠ *  - a special situation where there is a 5+card spade suit with a singleton Ace in another suit. The opener will consider this bid as a close-out bid, and will pass. The partnership with a 10+card spade fit will likely succeed in making the game contract.
     10-12 pts:  responder has 2 options:
        • Bid  3 ♠  - a double raise indicating the point count range. There are not quite enough combined partnership points for a game.
        • Bid  4 ♠ *  - a special situation where there is a 5+card spade suit with a singleton Ace in another suit. The opener will consider this bid as a close-out bid, and will pass. The partnership with a 10+card spade fit will likely succeed in making the game contract.
     13-16 pts:  There are enough partnership points for a game in spades. responder has 2 options:
        • Bid  4 ♠  with only a 3-card spade suit. This triple raise indicates both point count range and suit length. The opener will consider this bid as a close-out bid, and will pass.
        • Bid the  Jacoby 2 NT  - a special situation where there is opening count and a 4+card spade suit. This provides the opener the opportunity to explore a slam contract.
     17-20 pts:  There are enough partnership points for a game in spades.
        • Bid  3 NT  - This jump-shift raise indicates the responder's point count range, and provides the opener the options to play the contract in No Trump, play the contract in 4-Spades, or explore a slam contract.

The #2 priority is to propose the other major, the 4+card heart suit. Ignore the minor suits, and see if the opener also has a 4-card heart suit. An 8-card fit in hearts may still be possible so the partnership can play a contract in a major suit. Proposing a new 4+card heart suit is subject to the 1-over-1 restriction. When introducing a new suit, keep the bidding level as low as possible. If the responder has:

    • 6-9 pts:  Propose  1 NT  - The 1-over-1 restriction prohibits bidding a new suit at the 2-level. Instead of bidding PASS (which indicates 0 to 5 pts), the 1NT bid indicaties the point count range and no spade support. It says nothing about the other 3 suits. This keeps the bidding open for the opener.

    • 10-16 pts:  Propose  2 ♥  - This bid indicates no spade support, 10-16 points, and a 4+card heart suit. Since this bid is a new suit, the opener must respond.

    • 17-20 pts:  Propose  3 ♥  - This jump-shift indicates the responder's point count range and a 4+card heart suit at a low level. Since this bid is a new suit, the opener must respond.

The partnership will not be playing a major suit contract. The partnership is still looking for a suit to play.
With the 8 or more remaining cards in the responder's hand, there will be a better minor suit with at least 4+cards long. Propose that better minor suit.
When proposing a new 4+card suit, keep the bidding level as low as possible. The responder does not know if the opener will accept that suit, so leave room for additional bidding if necessary. If the responder has:
    • 6-9 pts:  Propose  1 NT  - The 1-over-1 restriction prohibits bidding a new minor suit at the 2-level. Instead of bidding PASS (which indicates 0 to 5 pts), the 1NT bid indicates the point count range and no spade support. It says nothing about the other 3 suits. This keeps the bidding open for the opener.
    • 10-16 pts:  Propose the Better Minor suit  2 ♣  or  2 ♦  - This bid indicates 10-16 points, no spade support, and no 4+card heart suit. The better minor suit will have at least 4+cards. Since this bid is a new suit, the opener must respond.
    • 17-20 pts:  Propose the Better Minor suit  3 ♣  or  3 ♦  - This jump-shift indicates the responder's point count range, no spade support, and no 4+card heart suit. The better minor suit will have at least 4+cards. This bid provides the opener the options to play the contract in No Trump, play the contract in the proposed minor, or explore a slam contract. Since this bid is a new suit, the opener must respond.