Why is there no traffic between vlans if the devices are on the same L3 Cisco Catalyst 3850 switch?

Question

Computer networks

There is a switch of the third level cisco 3850 with the IPBase license.
I connected a cisco aironet 2602I access point to port 3 and a computer to port 5.
Question - how to configure the switch so that I can see any subnet from wlan? All subnets are directly connected to the switch.
Brief description of the main configuration settings:
1 assigned vlan3 to manage access points and hung it on the 3rd port of the switch with ip address 192.168.3.1 255.255.255.0 (access point is given address 192.168.3.2)
2 assigned vlan 4 to WLAN and created an interface with ip 192.168.4.1 255.255.255.0 (wi-fi client is given 192.168.4.2)
3 vlan 5 assigned to Desktop which hung on the 5th switch port with ip 192.168.5.1 255.255.255.0 (Desktop Address 192.168.5.2)
The ip address of each vlan is a sort of default gateway for the subnet it belongs to.
Ip routing works. For example, from Desktopa with an ip address of 192.168.5.2, I see an access point with an address of 192.168.3.2 and vice versa, but for example, from a client that connected to wi-fi with an ip address of 192.168.4.2, I don’t see Desktop and vice versa. From the wi-fi network, only the addresses of the switch interfaces 192.168.3.1-4.1-.5.1 are visible.
Route table
3850#sh ip route
Codes: L - local, C - connected, S - static, R - RIP, M - mobile, B - BGP
D - EIGRP, EX - EIGRP external, O - OSPF, IA - OSPF inter area
N1 - OSPF NSSA external type 1, N2 - OSPF NSSA external type 2
E1 - OSPF external type 1, E2 - OSPF external type 2
i - IS-IS, su - IS-IS summary, L1 - IS-IS level-1, L2 - IS-IS level-2
ia - IS-IS inter area, * - candidate default, U - per-user static route
o - ODR, P - periodic downloaded static route, H - NHRP, l - LISP
+ - replicated route, % - next hop override
Gateway of last resort is not set
192.168.3.0/24 is variably subnetted, 2 subnets, 2 masks
C 192.168.3.0/24 is directly connected, Vlan3 L
192.168.3.1/32 is directly connected, Vlan3
192.168.4.0/24 is variably subnetted, 2 subnets, 2 masks
C
/32 is directly connected, Vlan4
192.168.5.0/24 is variably subnetted, 2 subnets, 2 masks
C 192.168.5.0/24 is directly connected, Vlan5
L 192.168.5.1/32 is directly connected, Vlan5
My config:
hostname 3850
!
boot-start-marker
boot-end-marker
!
!
!
!
username testing privilege 15 secret testing
no aaa new-model
switch 1 provision ws-c3850-24p
!
ip device tracking
!
IP routing
!
ip dhcp pool APs
network 192.168.3.0 255.255.255.0
default-router 192.168.3.1
dns-server 192.168.3.1
!
ip dhcp pool clients
network 192.168.4.0 255.255.255.0
default-router 192.168.4.1
dns-server 192.168.4.1
!
!
!
interface GigabitEthernet1/0/3
description CAPWAP AP
switchport access vlan 3
switchport mode access
!
interface GigabitEthernet1/0/5
description Desktop
switchport access vlan 5
switchport mode access
!
interface Vlan1
no ip address
shutdown
!
interface Vlan3
ip address 192.168.3.1 255.255.255.0
!
interface Vlan4
ip address 192.168.4.1 255.255.255.0
!
interface Vlan5
ip address 192.168.5.1 255.255.255.0
no ip http server
ip http authentication local
ip http secure-server
!
!
!
ip sla enable reaction-alerts
!
!
!
line con 0
logging synchronous
!
line vty 0 4
logging synchronous
login local
line vty 5 15
logging synchronous
login local
!
wireless mobility controller
!
wireless management interface Vlan3
!
wireless mgmt-via-wireless
!
wlan testing1234 1 testing1234
client vlan 4
no security wpa akm dot1x
security wpa akm psk set-key ascii 0 testing1234
no shutdown
end

Answer 1

The issue was resolved. At the moment the access point is connected to the controller, the CAPWAP interface with the trunk mode should rise, but it did not rise for some reason. So I completely reset the switch and set it up on a new one and it all worked.
Thanks to all

Answer 2

I haven't worked with a Cisco AP, but shouldn't gi1/0/3 be a trunk tagged with vlan 4?

Answer 3

Let's figure it out so that I understand everything correctly. You have 3850 and 3 subnets 3.1, 4.1, 5.1 are connected to it, on 5.1 we have a desktop, on 3.1 and 4.1 we have access points. And everything would be nothing but you do not see the Desktop when you connect to the network 4.0 (from 3.0 as I saw everything is visible)
What do you mean by the word "not visible"? Pings do not go? Tracing?