Filter tab file based on column value

Hello
I have a tab text file with many columns and have to filter rows ONLY if column 22 has the value of '0', '1', '2' or '3' (out of 0-5).

If Column 22 has value '0','1', '2' or '3' (highlighted below), then remove anything less than 10 and greater 100 (based on column 5) AND remove anything less than 5.0 (this column has decimals) (based on column 13).

I tried the following codes but I am not sure how to insert the condition of do the following only if column 22 has the following values of 0 to 3 and retain the other rows (ie that has values 4 and 5) as it is in the output file

awk -F "\t"  'NR==1; NR>1 {if ($5 > 10 && $5<100 && $13>5.0) print $0}' input.txt > output.txt
awk -F'\t' 'NR==1 || 0<=$22 && $22<=3 && 10<$5 && $5<100 && 5<$13' input > output

My input file is as follows

and

 Column1    ...    Column5    ...    Column13    ..    Column22    
ID1    a1            5                 0                5                
ID2    a2            10              1.2                0
ID3    a3            4                5.6                1
ID4    a4            300            2.6                2                
ID5    a5            40              32                0
ID6    a6            200             4.6                3
ID7    a7            200             4.5                5                
ID8    a8            3456           4.9                4                

and my desired output is

Column1 ..   Column5 ..   Column13 ..   Column22
ID1    a1            5                        0           5
ID5    a5            40                     32           0
ID7    a7            200                   4.5          5
ID8    a8            3456                 4.9         4

Any help is appreciated. Thank you

How about

awk 'NR == 1 || !(($22 <= 3) && ($5 < 10 || $5 > 100 || $13 < 5)) ;' file
Column1        Column5        Column13        Column22    
ID1    a1            5                 0                5                
ID5    a5            40              32                0
ID7    a7            200             4.5                5                
ID8    a8            3456           4.9                4
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