2 added 69 characters in body
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Charcoal, 172172 164 bytes

≔⁺⭆χιαα≔Φ↥S№αιθFθ«E⁵⭆⁵⎇﹪÷⍘”^=⪫Þ⭆z⁴‹⁻&,N8'↙¡⦄⍘>B⟧hζwlmt⮌C{WYMxW3-⁹Àm‖`η¡9⭆0λj≦$ï⊟du⊞qKMiΣF↥‴#ξ‖V“ωN|NF≧dD+=S9,*M⁹↘|^≧⮌Y✳Ihcχ·d⊕X№»s↶γ{WΠD⦃»M§⁷⁷”⁶²X²⁺μ×⁵⁺κ×⁵⌕α鲧θ⊖L⊞Oυω≔⁺⭆χιαα≔Φ↥S№αιθFθ«E⁵⭆§⪪”)∧%"<⁰ETV´el⟧2[◧À&η²p.±‹§K×GR←∨�X¶⌈hF)ξυ9DUuqε↘Z)s⎚H⊙←<¿.&]~b≧✂⪪XïJ61%ZWm/ειK⮌λ﹪▷(σΠNc←º✳Fb⌕⊘¹ÞEpM&➙δl◨α↑j≕ςL¡ρG⁰/y”⁵⁺κ×⁵⌕αι⎇Iμ§θ⊖L⊞Oυω M⁷±⁵

Try it online!Try it online! Link is to verbose version of code. Explanation:

≔⁺⭆χιαα

Prefix the digits to the predefined uppercase alphabet.

≔Φ↥S№αιθ

Uppercase the input and filter out all the unsupported characters.

Fθ«

Loop over the remaining characters.

E⁵⭆⁵E⁵

Double loop, joining the inner results into stringsLoop over each row, so that the result implicitly prints a 5×5 squareprinting each result on its own line.

⎇﹪÷⍘”⭆§⪪”...”⁶²X²⁺μ×⁵⁺κ×⁵⌕αι²”⁵⁺κ×⁵⌕αι

Extract the relevant bit fromThe compressed string is @ovs's large integer constant, which was converted to base 62binary and reversed. It is then compressed using Charcoal's compression anywaysliced into 180 substrings of 5 characters, and the relevant substring for the current character and row is then looped over.

§θ⊖L⊞Oυω⎇Iμ§θ⊖L⊞Oυω 

If the bit was set then cyclically print the next character of the filtered input otherwise print a space.

M⁷±⁵

Position the cursor ready to print the next character.

Charcoal, 172 bytes

≔⁺⭆χιαα≔Φ↥S№αιθFθ«E⁵⭆⁵⎇﹪÷⍘”^=⪫Þ⭆z⁴‹⁻&,N8'↙¡⦄⍘>B⟧hζwlmt⮌C{WYMxW3-⁹Àm‖`η¡9⭆0λj≦$ï⊟du⊞qKMiΣF↥‴#ξ‖V“ωN|NF≧dD+=S9,*M⁹↘|^≧⮌Y✳Ihcχ·d⊕X№»s↶γ{WΠD⦃»M§⁷⁷”⁶²X²⁺μ×⁵⁺κ×⁵⌕α鲧θ⊖L⊞Oυω M⁷±⁵

Try it online! Link is to verbose version of code. Explanation:

≔⁺⭆χιαα

Prefix the digits to the predefined uppercase alphabet.

≔Φ↥S№αιθ

Uppercase the input and filter out all the unsupported characters.

Fθ«

Loop over the remaining characters.

E⁵⭆⁵

Double loop, joining the inner results into strings, so that the result implicitly prints a 5×5 square.

⎇﹪÷⍘”...”⁶²X²⁺μ×⁵⁺κ×⁵⌕αι²

Extract the relevant bit from @ovs's large integer constant, which was converted to base 62 and then compressed using Charcoal's compression anyway.

§θ⊖L⊞Oυω 

If the bit was set then cyclically print the next character of the filtered input otherwise print a space.

M⁷±⁵

Position the cursor ready to print the next character.

Charcoal, 172 164 bytes

≔⁺⭆χιαα≔Φ↥S№αιθFθ«E⁵⭆§⪪”)∧%"<⁰ETV´el⟧2[◧À&η²p.±‹§K×GR←∨�X¶⌈hF)ξυ9DUuqε↘Z)s⎚H⊙←<¿.&]~b≧✂⪪XïJ61%ZWm/ειK⮌λ﹪▷(σΠNc←º✳Fb⌕⊘¹ÞEpM&➙δl◨α↑j≕ςL¡ρG⁰/y”⁵⁺κ×⁵⌕αι⎇Iμ§θ⊖L⊞Oυω M⁷±⁵

Try it online! Link is to verbose version of code. Explanation:

≔⁺⭆χιαα

Prefix the digits to the predefined uppercase alphabet.

≔Φ↥S№αιθ

Uppercase the input and filter out all the unsupported characters.

Fθ«

Loop over the remaining characters.

E⁵

Loop over each row, implicitly printing each result on its own line.

⭆§⪪”...”⁵⁺κ×⁵⌕αι

The compressed string is @ovs's large integer constant, converted to binary and reversed. It is then sliced into 180 substrings of 5 characters, and the relevant substring for the current character and row is then looped over.

⎇Iμ§θ⊖L⊞Oυω 

If the bit was set then cyclically print the next character of the filtered input otherwise print a space.

M⁷±⁵

Position the cursor ready to print the next character.

1
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Charcoal, 172 bytes

≔⁺⭆χιαα≔Φ↥S№αιθFθ«E⁵⭆⁵⎇﹪÷⍘”^=⪫Þ⭆z⁴‹⁻&,N8'↙¡⦄⍘>B⟧hζwlmt⮌C{WYMxW3-⁹Àm‖`η¡9⭆0λj≦$ï⊟du⊞qKMiΣF↥‴#ξ‖V“ωN|NF≧dD+=S9,*M⁹↘|^≧⮌Y✳Ihcχ·d⊕X№»s↶γ{WΠD⦃»M§⁷⁷”⁶²X²⁺μ×⁵⁺κ×⁵⌕α鲧θ⊖L⊞Oυω M⁷±⁵

Try it online! Link is to verbose version of code. Explanation:

≔⁺⭆χιαα

Prefix the digits to the predefined uppercase alphabet.

≔Φ↥S№αιθ

Uppercase the input and filter out all the unsupported characters.

Fθ«

Loop over the remaining characters.

E⁵⭆⁵

Double loop, joining the inner results into strings, so that the result implicitly prints a 5×5 square.

⎇﹪÷⍘”...”⁶²X²⁺μ×⁵⁺κ×⁵⌕αι²

Extract the relevant bit from @ovs's large integer constant, which was converted to base 62 and then compressed using Charcoal's compression anyway.

§θ⊖L⊞Oυω 

If the bit was set then cyclically print the next character of the filtered input otherwise print a space.

M⁷±⁵

Position the cursor ready to print the next character.